Question

What are the first four terms of a geometric sequence if its common ratio is 5 and its first term is 2.5?

2.5, 7.5, 12.5, 17.5
2.5, 0.5, 0.1, 0.02
2.5, 12.5, 62.5, 312.5
2.5, -2.5, -7.5, -12.5

Answer 1

C

Explanation:

I think

Answer 2

Answer: C: 2.5, 12.5, 62.5, 312.5

Explanation:

Let us remember that in a geometric sequence:

ratio =
`(a_(2) )/(a_(1))`

We know that
`a_(1)` (first term) is 2.5. So plug in the numbers into the above formula:

5 =
`(a_(2) )/(2.5)`

Multiply both sides by 2.5 to solve for
`a_(2)` (second term):

5 × 2.5 = 12.5

By process of elimination, it is obvious the correct answer is C.

We can double check your answer by checking the rate is 5 by dividing:

For example, 62.5 (
`a_(3)`) divided by 12.5 (
`a_(2)`) is appropriately 5.

Similarly, 312.5 (
`a_(4)`) divided by 32.5 (
`a_(3)`) is again 5, confirming our answer to be correct.