Answer to Question #150591 in Algebra for Cavahos Muhatmir

Question

An arithmetic sequence whose first term is 2 has the property that its second, third, and seventh terms are consecutive terms of a geometric sequence. Determine all possible second terms of the arithmetic sequence

Answer 1

To find an arithmetic sequence is to find a and d.

Its second, third and seventh terms are 2+d, 2+2d and 2+6d . Therefore

(2+2d)² = (2+d)(2+6d)

⇒ 4+8d+4d²=4+14d+6d²

⇒ 2d²+6d=0

⇒ d=0,−3

For Second terms d = 0 , -3

Second term 2 + d

i) 2 + 0 = 2

ii) 2 + (-3) = 2-3 = -1

2 , -1 are the possible second terms