Question

Which statement about the sequence -1,-5,-25,-125,... is true?

A. its arithmetic

B. its geometric

C. none

Answer 1

If a, b, c is an arithmetic sequence, then b - a = c - b.

If a, b, c is a geometric sequence, then b : a = c : b.

We have:

-1, -5, -25, -125, ...

Check the difference:

-5 - (-1) = -5 + 1 = -4

-25 - (-5) = -25 + 5 = -20

-4 ≠ -20

It's not an arithmetic sequence.

Check the quotient:

-5 : (-1) = 5

-25 : (-5) = 5

-125 : (-25) = 5

Therefore your answer is

B. It's geometric

Answer 2

B. its geometric

Explanation:

-1,-5,-25,-125,...

Take the 2nd term minus the 1st term, then the third term minus the 2nd term and so on

-5- -1 = -5+1 = -4

-25 --5 = -25+5 = -20

The terms are not the same so it is not arithmetic

Take the 2nd term and divide by the 1st term, then the third term divided by the second term and so on

-5/-1 = 5

-25/-5 = 5

-125/-25 = 5

The terms are the same so the sequence is geometric with a ratio of 5