The explicit rule for a sequence is an=7(−4)n−1 . what is the recursive rule for the sequence? an=−4(an−1),a1=7 an=−7(an−1),a1=4 an=−7(an+1),a1=4 an=−4(an+1),a1=7

Option (a) is correct.

The recursive rule for the given sequence is with

Step-by-step explanation:

The explicit sequence of the geometric sequence is given by:

where,  

is the first term

r is the common ratio  

n is the number of terms

For the given explicit rule,

Comparing with above sequence , we have,

and r = -4

Recursive formula for the geometric sequence having and r = -4  is given by:

Putting values, we get,

Hence, the recursive rule for the given sequence is with

hence, option (a) is correct.