Identify the 42nd term of an arithmetic sequence

Question

where a1=-12 and a27 = 66?

Answer 1

let A_27 = 66 so n= 27

Remember that a_n = a_1 + (n-1)dan=a1+(n−1)d

66 = -12 + (27 -1)d

66 = -12 + (26d)

66 + 12 = 26d

78 = 26d

d = 3

so to find A_42 use A1 = -12 , n = 42 and d = 3

where d is the common difference.

Then, use the same formula for n = 42

a_42 = -12 + ( 42 -1 ) * 3

a_42 = -12 + 41 * 3

a_42 = -12 + 123

a_42 = 111

42nd term of an arithmetic sequence is 111