Question

What should be the value of x so that the three consecutive terms will be in GP 2x+2, 16 and 64x. Also find the sum of first 10 terms if the starting term is 2x+2.

Answer 1

Answer:

x = 1 and -2

Sum of the first ten terms = 1,398,100

Step-by-step explanation:

Given the geometric progression 2x+2, 16, 64x...

Since they are in GP, their common ratio is expressed as;

16/2x+2 = 64x/16

16/2(x+1) = 4x

8/x+1 = 4x

Cross multiply

4x(x+1) = 8

4x²+4x = 8

4x²+4x - 8 = 0

divide through by 4

x²+x - 2 = 0

Factorize

x²+2x-x- 2 = 0

x(x+2)-1(x+2) = 0

(x-1)(x+2) = 0

x = 1 and -2

Hence the values of x are 1 and -2

Get the common ratio;

r = 16/2x+2

Since x = 1

r = 16/2(1)+2

r = 16/4

r = 4

Sum of the first n terms is expressed as;

Sn = a(rⁿ-1)/r-1

a = 2x+2

a = 2(1)+2

a = 4

Substitute;

S10 = 4(4^10 - 1)/4 - 1

S10 = 4(1,048,576-1)/3

S10 = 4,194,300/3

S10 = 1,398,100

Hence the sum of the first ten terms is 1,398,100