Question

The sum of first four terms is a G.P. is 30 and that of the last four terms is 960. if its first term is 2, find the common ratio.​

Answer 1

r = 2

Step-by-step explanation:

Let the first term be a.

(i)

Given that Sum of first four terms is 30 and First term is 2.

⇒ a + ar + ar² + ar³ = 30

⇒ a(1 + r + r² + r³) = 30

⇒ 2(1 + r + r² + r³) = 30

⇒ 1 + r + r² + r³ = 15.

(ii)

Given that Sum of last four terms is 960 and last term of GP is 512.

⇒ (512/r³) + (512/r²) + (512/r) + 512 = 960

⇒ 512(1/r³ + 1/r² + 1/r + 1) = 960

⇒ 512(1 + r + r² + r³) = 960 * r³

⇒ 512(15) = 960 * r³

⇒ 7680/960 = r³

⇒ 8 = r³

⇒ 2³ = r³

⇒ r = 2.

Therefore, Common ratio is 2.

Hope it helps!