In a geometric sequence with a1 = 5 and r = 2, what is a4?

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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 a4?

Explanation:
In a geometric sequence, each term is found by multiplying the previous term by the common ratio. The nth term can be written as a_n = a1 × r^(n−1). With a1 = 5 and r = 2, the fourth term is a4 = 5 × 2^(4−1) = 5 × 8 = 40. You can confirm the pattern by stepping through: a2 = 10, a3 = 20, a4 = 40. The other options don’t follow this doubling pattern from 5: 20 is the third term, 80 would be the fifth term, and 25 isn’t obtained by multiplying by 2 starting from 5.

In a geometric sequence, each term is found by multiplying the previous term by the common ratio. The nth term can be written as a_n = a1 × r^(n−1). With a1 = 5 and r = 2, the fourth term is a4 = 5 × 2^(4−1) = 5 × 8 = 40. You can confirm the pattern by stepping through: a2 = 10, a3 = 20, a4 = 40. The other options don’t follow this doubling pattern from 5: 20 is the third term, 80 would be the fifth term, and 25 isn’t obtained by multiplying by 2 starting from 5.

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