Question

Please solve the above sum (question no. 9)
Do it in a copy plz

Answer 1

125:152 is ratio and

Answer 2

Let a be the first term and r be the common ratio.

Given that Sum of first 3 terms to that of sum of first 6 terms is 125 : 152.

⇒ S₃ ÷ S₆ = 125/152

⇒ [a(r^3 - 1)/r - 1] * [r - 1/a(r^3 - 1)] = 125/152

⇒ r³ - 1/r⁶ - 1 = 125/152

⇒ (r³ - 1)/(r³ - 1)(r³ + 1) = 125/152

⇒ 1/r³ + 1 = 125/152

⇒ 152 = 125r³ + 125

⇒ 27 = 125r³

⇒ r³ = (27/125)

⇒ r³ = (3/5)^3

⇒ r = (3/5).

Therefore, Common ratio = (3/5).

Hope it helps!