Question

_____ 14. Tell whether the sequence is arithmetic, geometric, or neither.

Find the next three terms of the sequence. Type your answer in the blank to the left.

A. neither; 7, -20, 61

B. geometric;7, -20, 61

C. arithmetic;

D. geometric;

Answer 1

Given, r = {7, -20, 61...}
Find a relationship between the first three terms of the sequence:

The difference between 7 and -20 is \((-3)^3 = -27\)
The difference between -20 and 61 is \((-3)^4 = 81\)

Thus we can assume the next term of the sequence is
\(61 + (-3)^5 = 61 - 243 = -182\)

If \(-182\) is the next term of the sequence, then term following it is:
\(-182 + ((-3)^6 = -182 + 729 = 549\)

And the term following 549 is
\(549 + (-3)^7 = 549 - 2187 = -1638\)

In other words, the common difference between the terms is \((-3)^{n+2}\)
Which is neither arithmetic nor geometric