Identify the Sequence 1 , 2 , 4 , 8 , 16

Problem

1,2,4,8,16,…

Solution

1. Identify the first term of the sequence, which is (a_1)=1

2. Calculate the ratio between consecutive terms to determine if there is a common ratio.

3. Divide the second term by the first term: 2/1=2

4. Divide the third term by the second term: 4/2=2

5. Divide the fourth term by the third term: 8/4=2

6. Conclude that since the ratio between any two consecutive terms is a constant r=2 the sequence is a geometric sequence.

7. Determine the general formula for the nth term using (a_n)=(a_1)⋅r(n−1)

Final Answer

Geometric Sequence with *(a_n)=2(n−1)

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