Question

Identify the 42nd term of an arithmetic sequence where a1 = -12 and a27 = 66. (2 points)

70

72

111

114

Answer 1

111

Explanation:

a1= -12 and a27=66

using an = a1 + (n - 1) d

66= -12 + (27 - 1) (d)

66 + 122 = 26d

78 = 26d

divide

3 = d

now solve for the 42nd term again using an = a1 + (n - 1) d

a42 = -12 (42 - 1) (3)

= -12 (41) (3)

= -12 + 123

= 111

Answer 2

111.

Explanation:

The terms in an Arithmetic sequence are a1, a1 + d, a1 + 2d..... where a1 is the first term and d is the common difference,

Therefore for this sequence the common difference is (a27 - a1) / 26

= (66 - (-12) / 26

= 78/26

= 3.

The nth term an = a1 + (n - 1)d, so

the 42nd term a42 = -12 + (42-1)*3

= -12 + 123

= 111.