In a geometric sequence with a1 = 6 and r = 1/2, what is a5?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

In a geometric sequence with a1 = 6 and r = 1/2, what is a5?

Explanation:
In a geometric sequence, each term is found by multiplying the previous term by the constant ratio. The nth term is a1 times r^(n-1). So a5 = 6 * (1/2)^4 = 6 * 1/16 = 3/8. You can also see this by halving four times: 6 → 3 → 3/2 → 3/4 → 3/8. The result 3/8 is the value after four steps, not one of the earlier terms; for example, a4 is 3/4.

In a geometric sequence, each term is found by multiplying the previous term by the constant ratio. The nth term is a1 times r^(n-1). So a5 = 6 * (1/2)^4 = 6 * 1/16 = 3/8. You can also see this by halving four times: 6 → 3 → 3/2 → 3/4 → 3/8. The result 3/8 is the value after four steps, not one of the earlier terms; for example, a4 is 3/4.

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