Sum of the 1st 10 terms of a certain G.P. is equal to 244 times sum of the first 5 terms. Common difference is

S10 = 244S5

We know that their formula Sn = a(r^n – 1)/r – 1

Therefore,

a(r^10 – 1)/(r – 1) = 244a(r^5 – 1)/(r – 1)

r^10 – 1 = 244(r^5 – 1)

r^10 – 1 = 244r^5 – 244

(r^5)^2 – 1 = 244r^5 – 244

Let r^5 = y

y^2 – 1 = 244y – 244

y^2 – 1 – 244y + 244 = 0

y^2 – 244y + 243 = 0

(y – 243)(y – 1) = 0

Let y – 243 = 0

y = 243

Let y – 1 = 0

y = 1

Given that y = r5

When y = 243

r^5 = 243

r =5^√243

r = 3

When y = 1

r^5 = 1

r =5^√1

r = 1 (not suitable)

Therefore r = 3 and r ≠ 1 cause at GP not exchange the value