TMUA Sequences & Series 2

Question 1

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

Accepted Answer

n(n+1)/2

Answer

The sum 1 + 2 + 3 + ... + n equals n(n+1)/2, a standard result.

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

Using S∞ = a/(1−r): 12 = 4/(1−r) gives 1−r = 1/3, so r = 2/3.

Question 3

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

Accepted Answer

49

Answer

T_15 = 7 + (14)(3) = 7 + 42 = 49.

Question 4

Which of the following infinite geometric series converges?

Accepted Answer

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

Answer

The series 5 + 5/2 + 5/4 + ... has ratio r = 1/2, and |r| < 1 guarantees convergence.

Question 5

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

Accepted Answer

20

Answer

Using n(n+1)/2 = 210 gives n(n+1) = 420; since 20 × 21 = 420, n = 20.

(TMUA) Test of Mathematics for University Admission Practice Test