Grade 9 : Mathematics - 6. Sequences (Set 4)

Question 1

Week ($n$)	1	2	3	4
Total Savings ($S_n$)	$12	$17	$22	$27

Based on the weekly savings table above, which expression represents the total savings $S_n$ in dollars for week $n$?

Accepted Answer

A) $5n + 7$

Answer

B) $5n + 12$

Answer

C) $12n + 5$

Answer

D) $7n + 5$

Question 2

An arithmetic sequence has terms $14, 21, x, 35, 42$. What is the missing value $x$?

Accepted Answer

C) 28

Answer

A) 26

Answer

B) 27

Answer

D) 29

Question 3

A bouncing rubber ball reaches peak heights of 160 cm, 120 cm, 90 cm, and 67.5 cm on consecutive bounces.

What is the common ratio $r$ of this geometric sequence?

Accepted Answer

B) 0.75

Answer

A) 0.5

Answer

C) 0.8

Answer

D) 0.6

Question 4

Find the 15th term of the arithmetic sequence with first term $a = -4$ and common difference $d = 3$.

Accepted Answer

A) 38

Answer

B) 41

Answer

C) 35

Answer

D) 44

Question 5

Frame 1 uses 4 tile pieces, Frame 2 uses 7 tile pieces, Frame 3 uses 10 tile pieces, and Frame 4 uses 13 tile pieces.

How many tile pieces will be required to construct Frame 12?

Accepted Answer

C) 37

Answer

A) 34

Answer

B) 36

Answer

D) 40

Question 6

Which term of the arithmetic sequence $5, 11, 17, 23, \dots$ is equal to 119?

Accepted Answer

C) 20th term

Answer

A) 18th term

Answer

B) 19th term

Answer

D) 21st term

Question 7

Find the 8th term of the geometric sequence $3, 6, 12, 24, \dots$.

Accepted Answer

A) 384

Answer

B) 256

Answer

C) 768

Answer

D) 192

Question 8

The general term of a sequence is given by $a_n = n^2 + 1$. What is the 10th term of this sequence?

Accepted Answer

C) 101

Answer

A) 99

Answer

B) 100

Answer

D) 102

Question 9

A city express bus leaves the central hub every 12 minutes starting at 8:00 AM (8:00 AM, 8:12 AM, 8:24 AM, ...).

At what time will the 7th bus depart from the central hub?

Accepted Answer

B) 9:12 AM

Answer

A) 9:00 AM

Answer

C) 9:24 AM

Answer

D) 9:06 AM

Question 10

In an arithmetic sequence, the 4th term is 18 and the 10th term is 48. What is the common difference $d$?

Accepted Answer

B) 5

Answer

A) 4

Answer

C) 6

Answer

D) 7

Question 11

Week ($n$)	1	2	3	4
Total Savings ($S_n$)	$12	$17	$22	$27

Assuming linear growth per day, what will be the plant height on Day 10?

Accepted Answer

C) 30 cm

Answer

A) 27 cm

Answer

B) 28 cm

Answer

D) 33 cm

Question 12

Rule: Each term after the second term is calculated by adding the two preceding terms ($a_n = a_{n-1} + a_{n-2}$).

Find $x$ in the sequence: $3, 5, 8, 13, x, 34$.

Accepted Answer

C) 21

Answer

A) 19

Answer

B) 20

Answer

D) 22

Question 13

What is the 12th term of the arithmetic sequence $85, 78, 71, 64, \dots$?

Accepted Answer

A) 8

Answer

B) 15

Answer

C) 1

Answer

D) -2

Question 14

A bacterial culture initially has 6,400 cells at hour 0. The count halves every hour due to an antibiotic treatment.

What is the bacterial count at hour 6?

Accepted Answer

B) 100

Answer

A) 200

Answer

C) 50

Answer

D) 400

Question 15

Concentric circular running lanes have radii: Lane 1 = 20 m, Lane 2 = 22.5 m, Lane 3 = 25 m, Lane 4 = 27.5 m.

Following this arithmetic pattern, what is the radius of Lane 8?

Accepted Answer

B) 37.5 m

Answer

A) 35 m

Answer

C) 40 m

Answer

D) 36.5 m

Question 16

The $n$-th term of a sequence is $a_n = 2n^2 - 3$. What is the difference between the 5th term and the 3rd term ($a_5 - a_3$)?

Accepted Answer

A) 32

Answer

B) 28

Answer

C) 30

Answer

D) 34

Question 17

What is the 9th term of the geometric sequence $2, -4, 8, -16, 32, \dots$?

Accepted Answer

C) 512

Answer

A) -512

Answer

B) 256

Answer

D) -256

Question 18

Which term is the FIRST negative term in the arithmetic sequence $100, 93, 86, 79, \dots$?

Accepted Answer

B) 16th term

Answer

A) 15th term

Answer

C) 17th term

Answer

D) 14th term

Question 19

If the numbers $12, k, 28$ form three consecutive terms of an arithmetic sequence, find the value of $k$.

Accepted Answer

C) 20

Answer

A) 18

Answer

B) 19

Answer

D) 22

Question 20

Wooden blocks are arranged to build steps: Step 1 requires 3 blocks, Step 2 requires 6 blocks, Step 3 requires 10 blocks, Step 4 requires 15 blocks.

How many wooden blocks are required for Step 8 using the rule $T_n = \frac{(n+1)(n+2)}{2}$?

Accepted Answer

C) 45

Answer

A) 36

Answer

B) 40

Answer

D) 55

Grade 9 : Mathematics - 6. Sequences (Set 4)