In a sequence defined by a_n = 2^n, what is the 5th term?

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Question: In a sequence defined by a_n = 2^n, what is the 5th term?

Options:

Correct Answer: 16

Solution:

a_5 = 2^5 = 32.

In a sequence defined by a_n = 2^n, what is the 5th term?

In a sequence defined by a_n = 2^n, what is the 5th term?

Step 1: Identify the formula for the sequence, which is a_n = 2^n.
Step 2: Determine which term you need to find. In this case, we need the 5th term, so n = 5.
Step 3: Substitute n with 5 in the formula: a_5 = 2^5.
Step 4: Calculate 2 raised to the power of 5. This means multiplying 2 by itself 5 times: 2 * 2 * 2 * 2 * 2.
Step 5: Perform the multiplication: 2 * 2 = 4, then 4 * 2 = 8, then 8 * 2 = 16, and finally 16 * 2 = 32.
Step 6: Conclude that the 5th term a_5 is equal to 32.

Exponential Sequences – Understanding how to evaluate terms in a sequence defined by an exponential function.