If x and 2 squareroot 2x4 are the first and fourth terms of

If x and 2 squareroot 2x^4 are the first and fourth terms of a geometric sequence, determine the seventh term.

first term a1 = 4

4th term a4 = 2 sqrt 2x^4

geometric sequence is given by the formula

An = a1 r^(n-1 )

A4 = a1 r ^ ( 4-1 )

2 sqrt 2x^4 = x r^3

squaring both sides

( 2 sqrt 2x^4 )^2 = (xr^3)^2

4 (2x^4 ) = x^2 r^6

dividing both sides by x^2

8 x^2 = r^6

r = ( 8x^2 )^1/6

hence, 7th term is

A7 = x ( ( 8x^2 )^1/6 ) ^ 6

A7 = x ( 8x^2 )

seventh term is = 8x^3