Question

the sum of first four terms of a GP is 30 and that of last four terms is 960. if the first and last term of gp are 2 and 512 respectively, find the common ratio.

Answer 1

Answer:

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!

Answer 2

Step-by-step explanation:

Let common ratio = r & number of terms = n

512/2 = 256 = 2^8 (because all terms will be divided by powers of 2 for common ratio )

=> r = 2 and n = 8

2,4,8,16,32,64,128,256,512

Sum of first four terms = 2+4+8+16=30

Sum of last four terms = 64+128+256+512=960