In a geometric sequence with a1 = 5 and r = 2, what is a3?

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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 = 5 and r = 2, what is a3?

Explanation:
In a geometric sequence, each term is found by multiplying the previous term by the constant ratio. The nth term can be written as a1 times r^(n−1). Here, a1 = 5 and r = 2, so a3 = 5 * 2^(3−1) = 5 * 4 = 20. You can verify by stepping through: a2 = 5*2 = 10, then a3 = 10*2 = 20. So the third term is 20. The other values don’t fit this pattern: 5 is the first term, 40 would be the fourth term, and 25 isn’t produced by doubling from 5.

In a geometric sequence, each term is found by multiplying the previous term by the constant ratio. The nth term can be written as a1 times r^(n−1). Here, a1 = 5 and r = 2, so a3 = 5 * 2^(3−1) = 5 * 4 = 20. You can verify by stepping through: a2 = 52 = 10, then a3 = 102 = 20. So the third term is 20. The other values don’t fit this pattern: 5 is the first term, 40 would be the fourth term, and 25 isn’t produced by doubling from 5.

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