In the geometric sequence with a1 = 2 and r = 3, what is a2?

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Multiple Choice

In the geometric sequence with a1 = 2 and r = 3, what is a2?

Explanation:
In a geometric sequence, each term is found by multiplying the previous term by the common ratio. Here, the first term is 2 and the ratio is 3, so the second term is obtained by multiplying the first term by 3: a2 = 2 × 3 = 6. You can also use the formula a_n = a1 × r^(n−1); for n = 2 this gives a2 = 2 × 3^(1) = 6. The other values don’t fit because they would require a different multiplier (for example, 4 would need multiplying by 2, 9 would need 4.5, and 12 would need 6), but the ratio is fixed at 3.

In a geometric sequence, each term is found by multiplying the previous term by the common ratio. Here, the first term is 2 and the ratio is 3, so the second term is obtained by multiplying the first term by 3: a2 = 2 × 3 = 6. You can also use the formula a_n = a1 × r^(n−1); for n = 2 this gives a2 = 2 × 3^(1) = 6. The other values don’t fit because they would require a different multiplier (for example, 4 would need multiplying by 2, 9 would need 4.5, and 12 would need 6), but the ratio is fixed at 3.

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