Question

If the nth partial sum of the sequence an is given by

n
Sigma 2k+4
k=1

Then what is the nth term of the sequence?
A. 6
B. 2n+4
C. 6+8+10+12+...+(2n+4)
D. 2(1)+4+2(n)+4

Answer 1

B-2n+4

Explanation:

Answer 2

This is an example of a series in arithmetic progression.

The nth term an can be calculated using the formula:

an = a1 + (n – 1) d

where: a1 = is the 1st term of the series

d = common difference

Calculating for the 1st term:

a1 = 2k + 4 = 2 (1) + 4 = 6

Calculating for the common difference by :

d = a2 – a1

d = 2 (2) + 4 – 6

d = 2

Therefore calculating for an:

an = 6 + (n – 1) 2

an = 6 + 2n -2

an = 2n + 4

Therefore the answer is B. 2n+4