What is the sum of the first 6 terms of an arithmetic progression with a1 = 3 and a6 = 15?

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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

What is the sum of the first 6 terms of an arithmetic progression with a1 = 3 and a6 = 15?

Explanation:
In an arithmetic progression, pairing terms from opposite ends adds to the same total. For six terms, you can group them as (a1 + a6), (a2 + a5), and (a3 + a4). Each pair adds up to a1 + a6 because a2 = a1 + d and a5 = a6 − d, so their sum is a1 + a6. Here a1 is 3 and a6 is 15, so each pair is 18. With three pairs, the total sum is 3 × 18 = 54. Therefore, the sum of the first six terms is 54.

In an arithmetic progression, pairing terms from opposite ends adds to the same total. For six terms, you can group them as (a1 + a6), (a2 + a5), and (a3 + a4). Each pair adds up to a1 + a6 because a2 = a1 + d and a5 = a6 − d, so their sum is a1 + a6. Here a1 is 3 and a6 is 15, so each pair is 18. With three pairs, the total sum is 3 × 18 = 54. Therefore, the sum of the first six terms is 54.

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