What is the 7th term of the sequence defined by a_n = 2^n + 3^n?

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Question: What is the 7th term of the sequence defined by a_n = 2^n + 3^n?

Options:

Correct Answer: 2187

Solution:

a_7 = 2^7 + 3^7 = 128 + 2187 = 2315.

What is the 7th term of the sequence defined by a_n = 2^n + 3^n?

What is the 7th term of the sequence defined by a_n = 2^n + 3^n?

Step 1: Identify the formula for the sequence, which is a_n = 2^n + 3^n.
Step 2: Determine the value of n for the 7th term, which is n = 7.
Step 3: Substitute n = 7 into the formula: a_7 = 2^7 + 3^7.
Step 4: Calculate 2^7. This means 2 multiplied by itself 7 times, which equals 128.
Step 5: Calculate 3^7. This means 3 multiplied by itself 7 times, which equals 2187.
Step 6: Add the results from Step 4 and Step 5: 128 + 2187.
Step 7: The final result is 2315, which is the 7th term of the sequence.

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