TMUA Sequences & Series 2

Question 1

Which formula gives the sum of the first n natural numbers?

Accepted Answer

n(n+1)/2

Answer

n(n−1)/2

Answer

n²/2

Answer

n(n+2)/2

Question 2

The sum to infinity of a geometric series is 12 and the first term is 4. What is the common ratio?

Accepted Answer

2/3

Answer

1/2

Answer

1/3

Answer

3/4

Question 3

Find the 15th term of the arithmetic sequence: 7, 10, 13, 16, ...

Accepted Answer

49

Answer

46

Answer

52

Answer

43

Question 4

Which of the following infinite geometric series converges?

Accepted Answer

5 + 5/2 + 5/4 + ...

Answer

2 + 4 + 8 + ...

Answer

3 − 6 + 12 − ...

Answer

1 + 1 + 1 + ...

Question 5

If the sum ∑_{k=1}^{n} k = 210, what is the value of n?

Accepted Answer

20

Answer

18

Answer

19

Answer

21

Question 6

A sequence is defined by a₁ = 2 and a_{n+1} = 3a_n − 1. What is the value of a₄?

Accepted Answer

41

Answer

38

Answer

44

Answer

35

Question 7

The sum of the first 5 terms of a geometric sequence with common ratio 2 is 31. What is the first term?

Accepted Answer

1

Answer

2

Answer

3

Answer

4