Determine the value of x that makes 2, 6, 5x - 2, ... a geometric sequence.

Question

Determine the value of x that makes 2, 6, 5x - 2, ... a geometric sequence.

Please answer in an organized and neat/easy to read format. And please only include the information that would be understood by a Grade 11. Thank you :)

Answer 1

2,6,5x-2 is a GP with r=3

2,6,18

5x-2 = 18

5x = 20

x = 4

Answer 2

For that to be a geometric sequence, the next term in the sequence must be a constant multiple

of the current term, so since a₁ = the first term in the sequence = 2 and a₂ = the second term in

the sequence = 6, then the multiple that we need is a₂ / a₁ = 6 / 2 = 3, so a₃ = the third term in

the sequence must be = 3 * a₂ = 3 * 6 = 18, but by what we are given a₃ also = 5x - 2,

so we have that 5x - 2 = 18, so 5x = 20, so x = 4.

Answer 3

5x - 2 = 6/2·6; 5x - 2 = 18; x = 4