Question

Given the following sequence, find the 23rd term: 3, 5, 7, 9, 11, . . .

A. 50
B. 47
C. 25
D. 26

Answer 1

B. 47

Explanation:

The sequence goes up by 2 each time, so to find the nth term, start with 2n.

For n = 1, 2n = 2(1) = 2, but we need 3, so modify to 2n + 1.

For n = 1, 2n + 1 = 2(1) + 1 = 2 + 1 = 3

For n = 2, 2n + 1 = 2(2) + 1 = 4 + 1 = 5

For n = 3, 2n + 1 = 2(3) + 1 = 6 + 1 = 7

Try n = 4 and 5, and you will get 9 and 11, respectively.

2n + 1 works for any term n, where n is natural number.

For the 23rd term, n = 23.

2n + 1 = 2(23) + 1 = 46 + 1 = 47

Answer: B. 47

Answer 2

B. 47

Explanation:

The formula for an arithmetic sequence is

an = a1+d(n-1)

a1 =3 (it is the first term)

We can find the common difference by taking the second term and subtracting the first term

5-3 =2

d=2

n = the term number we are looking for

an = 3 + 2(n-1)

We are looking for the 23rd term so n=23

a23 = 3 +2(23-1)

= 3 +2(22)

= 3+44

= 47