Identify the type of sequence shown in the table below and select the appropriate response. n f(n) 1 48 2 −96 3 192 4 −384 5 768 arithmetic sequence; common difference is 96 arithmetic sequence; common difference is −144 geometric sequence; common ratio is 3 geometric sequence; common ratio is −2

This is a geometric sequence with common ratio r = - 2

r = = = = - 2

the sequence is geometric sequence with common ratio (-2).

Option : D is correct.

Step-by-step explanation:

In this question table is given as

n          1          2         3           4            5

f(n)     48       -96      192      -385       768

We have to find out if the sequence is arithmetic or geometric.

For Arithmetic sequence :

Difference should be common in each term of fees.

common difference = f(2) - f(1)

= -96 -48 = -144

similarly = f(3) - f (2) = 192 + 96 = 288

Here, ≠ so the sequence is not an arithmetic sequence.

For Geometric sequence :

Ratio  should be common in each term of f(n)

Common ratio =

Therefore, the sequence is geometric sequence with common ratio (-2).

Option : D is correct.