MCQ Questions

Question No. 1

Write down the next three terms for each of the following number sequences.

Answer :

a) 2, 4, 6, 8, …

b) 99, 97, 95, 93, …

c) 4, 12, 36, 108, …

d) 81, 27, 9, 3, …

e) 1, −2, 3, −4, 5, …

f) 1, 4, 9, 16, …

g) 1, 1, 2, 3, 5, 8, …

h) 3, 6, 11, 18, 27, …

i) p, p², p³, p⁴, …

j) a − b, 2a − 2b, 3a − 4b, 4a − 8b, …

Question No. 2

For each of the following number patterns, say whether it is an arithmetic progression or not. If it is an arithmetic progression, write down the common difference.

Question No. 3

Write down the first five terms of the arithmetic progression of which:

Answer :

a) the first term is 3 and the common difference is 9

b) the first term is 71 and the common difference is −10

c) the first term is 8.1 and the common difference is −0.2

d) the first term is −25 and the common difference is 3

e) the first term is xy and the common difference is 2xy

Question No. 4

Write down the next three terms of each of the following arithmetic progressions.

Answer :

a) −4, 3, 10, 17, …

b) 5, 1, −3, −7, …

c) −100, −82, −64, −46, …

d) 5.5, 5.7, 5.9, 6.1, …

e) 4p − 3q, 3p − 2q, 2p − q, p, …

Question No. 5

Find the formula (in its simplest form) for the nth term of each of the following arithmetic progressions, if:

Answer :

a) a = 1, d = 7 → aₙ = 1 + 7(n−1)

b) a = 13, d = −3 → aₙ = 13 − 3(n−1)

c) a = −11, d = 2 → aₙ = −11 + 2(n−1)

d) a = 2, d = ½ → aₙ = 2 + ½(n−1)

e) a = 42, d = −2.5 → aₙ = 42 − 2.5(n−1)

f) a = x, d = x → aₙ = x + x(n−1)

Question No. 6

Find the formula for the nth term of each of the following arithmetic progressions. Write your answers in their simplest form.

Answer :

a) 11, 14, 17, 20, … → aₙ = 11 + 3(n−1)

b) 1, 8, 15, 22, … → aₙ = 1 + 7(n−1)

c) −4, 1, 6, 11, … → aₙ = −4 + 5(n−1)

d) 39, 29, 19, 9, … → aₙ = 39 − 10(n−1)

e) −6, −5.6, −5.2, −4.8, … → aₙ = −6 + 0.4(n−1)

f) 8, 7.5, 7, 6.5, … → aₙ = 8 − 0.5(n−1)

Question No. 7

Calculate the first term and the common difference of an arithmetic progression, if the nth term of the progression is given by the formula:

Answer :

a) Tₙ = 2n + 6

b) Tₙ = −n + 2.5

c) Tₙ = −3n − 10

d) Tₙ = ½n + ¾

e) Tₙ = 15 − 13n

f) Tₙ = 1.6n − 0.8

Question No. 8

Calculate the number of terms in each of the following arithmetic progressions.

Answer :

a) Tₙ = 5n − 21, last term = 99

b) Tₙ = −n + 3, last term = −27

c) Tₙ = −7n + 9, last term = −327

d) Tₙ = 3.5n + 8.5, last term = 166

Question No. 9

The nth term of an arithmetic progression is given by the formula Tₙ = 2n + 13.

Answer :

a) Find the 61st term.

b) Which term is equal to 61?

Question No. 10

If the 12th term of an arithmetic progression is −99 and the 30th term is 63, calculate:

Answer :

a) the first term and the common difference

b) the 17th term

c) the number of terms in the progression, if the last term is 0

Question No. 11

The last two terms of an arithmetic progression are 10 and 2. If there are 32 terms in the progression, find the 16th term.

Answer :

Question No. 12

Find the arithmetic mean of the following pairs of numbers.

Answer :

a) 10 and 48

b) −14 and 0

c) −21 and 19

d) ¼ and ¾

e) 0.6 and 3.5

f) −12.2 and 16.8

g) −362 and −204

h) 5/6 and 6/7

Question No. 13

Insert two arithmetic means between 32 and 53.

Answer :

Question No. 14

Insert five arithmetic means between −18.5 and −5.

Answer :

Question No. 15

Find the sum of the first 20 terms of each arithmetic progression.

Answer :

a) 2, 11, 20, 29, …

b) 40, 30, 20, 10, …

c) 7.5, 14, 20.5, 27, …

d) 342, 302, 262, 222, …

e) −51, −48, −45, −42, …

f) 63, 56, 49, 42, …

Question No. 16

Find the sum of the first 49 terms of each arithmetic progression.

Answer :

a) 17, 16, 15, 14, …

b) 92, 110, 128, 146, …

c) 64.2, 63.8, 63.4, 63.0, …

d) −750, −725, −700, −675, …

e) 2.5, 1.0, −0.5, −2.0, …

f) −11.0, −8.9, −6.8, −4.7, …

Question No. 17

Find the sum of each arithmetic progression for which the first and last terms are given.

Answer :

a) T₁ = 15 and T₃₅ = 899

b) T₁ = −22 and T₁₇ = 122

c) T₁ = 4.4 and T₂₇ = 85

d) T₁ = −183 and T₁₅ = −1

e) T₁ = −0.3 and T₆₁ = 23.7

f) T₁ = 192 and T₃₅ = 362

Question No. 18

Calculate each of the following series.

Answer :

a) 1 + 2 + 3 + 4 + … + 999

b) 3 + 9 + 15 + 21 + … + 195

c) 1.25 + 1.5 + 1.75 + 2 + … + 23.5

d) −15 − 17 − 19 − 21 − … − 73

e) 105 + 78 + 51 + 24 + … − 840

f) 100 − 4 + 99 − 8 + 98 − 12 + … + 1 − 400

Question No. 19

Coins are arranged in piles. The first pile contains six coins and each successive pile contains two more coins than the previous one.

Answer :

a) How many coins will the 20th pile contain?

b) How many coins will there be in the first 50 piles?

c) What pile will contain 300 coins?

Question No. 20

In a competition, the prize money is divided as follows. The person in tenth place gets ₦2 500 and every other prize winner gets ₦1 500 more than the person who finished just after them. Prizes are awarded for the top ten places.

Answer :

a) How much money does the winner get?

b) In what place does the person who gets ₦10 000 finish?

c) What is the total prize money for the event?

Question No. 21

After being injured in a football match, a player was advised to start a gradual jogging programme. In the first week, he must jog for ten minutes each day for six days of the week. Each week after that, he must jog for five minutes more every day for six days of the week.

Answer :

a) How many minutes will he jog in the first week?

b) How many minutes will he jog in the second week?

c) How many minutes will he have jogged altogether by the end of the ninth week?

Question No. 22

Bimpe is working hard to save money. Every week, she saves ₦500 more than in the previous week. In the first 10 weeks, she saves ₦35 000 in total.

Answer :

a) How much money did she save in the first week?

b) How much will she have saved altogether by the end of the first year? (52 weeks)

Question No. 23

You are given the following information: The sum of the interior angles of a triangle is 180°, quadrilateral 360°, pentagon 540°.

Answer :

a) Explain why these angle sums form an arithmetic progression.

b) Calculate the sum of the interior angles of a dodecagon (12 sides).

c) How many sides does a polygon have if the sum of its angles is 5 400°?

Question No. 24

For each of the following number patterns, say whether it is a geometric progression or not. If it is a geometric progression, write down the first term and the common ratio.

Question No. 25

Write down the first five terms of the geometric progression of which:

Answer :

a) the first term is 1 and the common ratio is 4

b) the first term is 81 and the common ratio is ⅓

c) the first term is 7 and the common ratio is 7

d) the first term is 625 and the common ratio is 0.2

e) the first term is xy and the common ratio is 2xy

Question No. 26

Write down the next three terms of each geometric progression.

Answer :

a) 8, 16, 32, 64, …

b) −1.5, −3, −6, −12, …

c) −2 187, 729, −243, 81, …

d) 0.24, 1.2, 6, 30, …

e) a/b, a²/(2b), a³/(4b), a⁴/(8b), …

Question No. 27

Find the formula (in its simplest form) for the nth term of each of the following geometric progressions, if:

Answer :

a) a = 1 and r = 7

b) a = 5 and r = −2

c) a = −10 and r = 3

d) a = 32 and r = ½

e) a = −9 and r = ⅓

f) a = x and r = x²

Question No. 28

Find the formula for the nth term of each geometric progression. Write your answers in their simplest form.

Answer :

a) 1, 2, 4, …

b) 5, 10, 20, …

c) 20, 30, 45, …

d) 100, 10, 1, …

e) 2.5, 25, 250, …

f) 1, 0.1, 0.01, …

Question No. 29

Show that the nth term of the geometric progression −256, 64, −16, … is given by the formula Tₙ = (−1) × 4⁵⁻ⁿ.

Answer :

Question No. 30

Calculate the first term and the common ratio of a geometric progression, if the nth term of the progression is given by the formula:

Answer :

a) Tₙ = 4 × 5ⁿ⁻¹

b) Tₙ = −6 × 2ⁿ

c) Tₙ = 7 × (−2)ⁿ⁻¹

d) Tₙ = 8ⁿ⁻¹

e) Tₙ = (−2.5)ⁿ

f) Tₙ = 10 × (½)ⁿ⁻¹

Question No. 31

Calculate the number of terms in each of the following geometric progressions, if:

Answer :

a) Tₙ = 80 × (½)ⁿ⁻¹ and the last term is 5/8

b) Tₙ = (−2)ⁿ⁻¹ and the last term is −512

c) Tₙ = −6 × 4ⁿ⁻¹ and the last term is −6 144

d) Tₙ = 1.5 × 3ⁿ⁻¹ and the last term is 364.5

Question No. 32

The nth term of a geometric progression is given by the formula Tₙ = 1.5ⁿ.

Answer :

a) Find the fifth term.

b) Which term is equal to 2187/128 ?

Question No. 33

If the sixth term of a geometric progression is 320 and the 11th term is 10 240, calculate:

Answer :

a) the first term and the common ratio

b) the fourth term

c) the number of terms in the progression, if the last term is 20 480

Question No. 34

The last two terms of a geometric progression are 96 and 192. If there are 9 terms in the progression, find the fifth term.

Answer :

Question No. 35

Find two possible values for the geometric mean, x, of:

Answer :

a) 9 and 81

b) 16 and 1

c) −20 and −5

d) 1/9 and 1

e) 3.5 and 14

f) 25/3 and 1/3

g) 153 and 17

h) −0.2 and −3.2

Question No. 36

Insert two geometric means between:

Answer :

b) −337.5 and −0.1

a) 4 and 108

Question No. 37

Insert three geometric means between 22 and 111.375. Find all the possibilities.

Answer :

Question No. 38

Find the sum of the first 20 terms of each geometric progression:

Answer :

a) 1, 2, 4, 8, …

b) 6, −12, 24, −48, …

c) 5, 1, 0.2, 0.04, …

d) −3, −1, −1/3, −1/9, …

e) 70, 35, 17.5, 8.75, …

f) 7, 1, 1/7, …

Question No. 39

Given the geometric progression −100, −50, −25, …:

Answer :

a) Find the sum of the first 5 terms.

b) Find the sum of the first 10 terms.

c) Find the sum of the first 20 terms.

d) What do you notice about your answers to questions a), b) and c)?

Question No. 40

Which of the following geometric progressions will have a sum to infinity? Give a reason for your answer each time.

Question No. 41

Find the sum to infinity of each of the convergent geometric progressions in question 1.

Answer :

Question No. 42

Find the first three terms of the geometric progression of which the common ratio is −0.2 and the sum to infinity is 5.

Answer :

Question No. 43

A rabbit colony started out with a pair of rabbits that had babies. If the size of the colony doubled every three weeks, what was the size of the colony after 30 weeks?

Answer :

Question No. 44

During an outbreak of the Ebola virus, health workers gathered the following information: by the end of the first week 982 people were infected; thereafter the number increased by 9% per day. Approximately how many people were infected by the end of the second week? Round to the nearest whole number.

Answer :

Question No. 45

A child dropped a ball from a first-floor balcony. It fell 5 m to the ground and thereafter bounced along the road. If the height of every bounce was 2/3 of the previous height, how far had the ball travelled by the time it came to rest? Round to the nearest metre.

Answer :

Question No. 46

Abayomi obtained 46% in his first math test and aimed to improve by 10% in each subsequent test. How many tests must he take to reach at least 80%?

Answer :

Question No. 47

A mine worker discovered an ore sample containing 650 mg of radioactive material with a half-life of two days. Calculate the amount of radioactive material remaining after two weeks.

Answer :

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