Identify the Sequence 8 , -16 , 32 , -64 , 128

Problem

8,−16,32,−64,128,…

Solution

1. Identify the first term of the sequence.

(a_1)=8

2. Calculate the ratio between consecutive terms to determine if it is a geometric sequence.

(−16)/8=−2

32/(−16)=−2

(−64)/32=−2

3. Determine the common ratio since the ratio between any two consecutive terms is constant.

r=−2

4. Apply the formula for the nth term of a geometric sequence, which is (a_n)=(a_1)⋅r^(n−1)

(a_n)=8⋅(−2)^(n−1)

Final Answer

Geometric Sequence with *(a_1)=8* and *r=−2

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