If first term of non-constant GP be 1/8 and every term is AM of next two

Question

If first term of non-constant GP be \(\frac {1}{8}\)and every term is AM of next two, then \(\displaystyle\sum_{r=1}^{20} T_r -\displaystyle\sum_{r=1}^{18} T_r\) is

(1) 2¹⁵ 

(2) -2¹⁵ 

(3) -2¹⁸ 

(4) 2¹⁸

Answer 1

Correct option is (2) -2¹⁵ 

\(a_1 = \frac {1}{8}\)

a, ar, ar², ar³ …… 

2ar = ar² + ar³ 

2 = r + r² 

r² + r – 2 = 0

\(r \ne 1\)

⇒ r = –2