Sequences and Series

Sequences and Series​

By Dr Kee

Multiple Choice

1.    The sequence 3, 12, 48, 192,… has

• a common ratio of 3

• a common difference of 3

• a common ratio of 4

• a common difference of 4

Multiple Choice

2.    The sequence 32, -8, 2, -0.5 ,… has

• a common ratio of 1/4

• a common difference of 1/4

• a common ratio of -1/4

• a common difference of -1/4

Fill in the Blanks

3.    The next term in the sequence 5, 12, 19, 26 is

Fill in the Blanks

4.    The next term in the sequence 64, 16, 4, 1 is

Fill in the Blanks

5.    What is the common difference in this arithmetic sequence: 4, __, __,__, 25

Fill in the Blanks

6.    What is the common ratio in this geometric sequence: 4, __, __, 108

Fill in the Blanks

7.    What is the common ratio in this geometric sequence: 32, __, __, __, 2

Fill in the Blanks

8.  $a_1=-8$      and   $d=4$  find $S_9$  

Fill in the Blanks

9. $a_1=4$   and $r=-3$  , find $S_7$  

Fill in the Blanks

10. $\sum_{n=4}^83n=$  

Fill in the Blanks

11. $\sum_{n=1}^92n-5=$  

Fill in the Blanks

12. $\sum_{n=1}^{\infty}4\left(-\frac{1}{2}\right)^{n-1}=$  

Fill in the Blanks

13. Find the fifth terms of $a_n=2a_{n-1}$   given $a_1=3$  

Fill in the Blanks

14. Find the fifth terms of $a_n=a_{n-1}+a_{n-2}$  , given $a_1=2,\ a_2=8$  

Multiple Choice

15. The sequence 1,1,2,3,5,8,... is

• arithmetic

• geometric

• Fibonacci

• None of the above

Fill in the Blanks

16. Given the sequence 2, _ , _ , -16

What is the missing third term if the sequence were Geometric?

Fill in the Blanks

17. Given the sequence 2, _ , _ , -16

What is the missing third term if the sequence were Arithmetic?

Fill in the Blanks

18.    Given the geometric sequence of 5, -15, 45, -135, …

What is $a_8$  ?

Fill in the Blanks

19.    Given the geometric sequence of 5, -15, 45, -135, …

What is $S_8$  ?

Open Ended

20.    You are offered a temporary job working for a company for 20 days. The company offers to pay you (A) $1500 per day or (B) 1/2 cent the first day and double the pay each day thereafter.

How much money do you make in 20 days of pay A?

Open Ended

21.    You are offered a temporary job working for a company for 20 days. The company offers to pay you (A) $1500 per day or (B) 1/2 cent the first day and double the pay each day thereafter.

How much money do you make in 20 days of pay B?