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

Since it is a geometric sequence, then multiplication is the process. 2 x 3 = 6, 6 x 3 = 18.

5x - 2 = 18

5x = 20

therefore, x = 4

Answer 2

definition of geometric sequence is from term to term the division is same result

t₂/t₁=t₃/t₂=.....

here t₂/t₁=3

so (5x-2)/6=3 is the requirement

x = 4 and term 3 is equal to 18

term four (just to look) must be t₄/18=3,,,,, term four is 54...