Identify the Sequence 2 , 4 , 8 , 16 , 64

Problem

2,4,8,16,64

Solution

1. Identify the terms of the given sequence as (a_1)=2 (a_2)=4 (a_3)=8 (a_4)=16 and (a_5)=64

2. Check for a common ratio by dividing consecutive terms.

3. Calculate the ratio between the first four terms:

4/2=2

8/4=2

16/8=2

4. Calculate the ratio between the fourth and fifth terms:

64/16=4

5. Conclude that because the ratio is not constant (2≠4, the sequence is neither arithmetic nor geometric. It appears to be a list of powers of 2 specifically 2,2,2,2,2 but it skips 2=32

Final Answer

The sequence *2,4,8,16,64* is a non-geometric sequence of powers of 2.

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