In an arithmetic progression with first term 2 and common difference 3, what is the fifth term?

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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 an arithmetic progression with first term 2 and common difference 3, what is the fifth term?

Explanation:
Think of an arithmetic progression as a sequence where you add the same amount each time. The nth term is found by a1 + (n−1)d. Here a1 is 2 and the common difference d is 3. For the fifth term: 2 + (5−1)×3 = 2 + 12 = 14. Listing the terms confirms it: 2, 5, 8, 11, 14. So the fifth term is 14, which matches the correct value among the choices. The other numbers would correspond to other positions (11 is the fourth, 17 is the sixth, 20 is the seventh).

Think of an arithmetic progression as a sequence where you add the same amount each time. The nth term is found by a1 + (n−1)d. Here a1 is 2 and the common difference d is 3. For the fifth term: 2 + (5−1)×3 = 2 + 12 = 14. Listing the terms confirms it: 2, 5, 8, 11, 14. So the fifth term is 14, which matches the correct value among the choices. The other numbers would correspond to other positions (11 is the fourth, 17 is the sixth, 20 is the seventh).

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