In an arithmetic sequence, the 3rd term is 10 and the 7th term is 26. What is the 15th term?
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Correct answer
C. 58
Principle or equation
For an arithmetic sequence, the nth term is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference. Given two terms, solve for a_1 and d.
Why this answer is correct
Let a_1 be the first term and d the common difference. We have a_3 = a_1 + 2d = 10 and a_7 = a_1 + 6d = 26. Subtracting the first from the second gives 4d = 16, so d = 4. Then a_1 = 10 - 2*4 = 2. The 15th term is a_15 = 2 + 14*4 = 2 + 56 = 58.
Example
If a_2 = 5 and a_5 = 14, then d = (14-5)/3 = 3, a_1 = 2, and a_10 = 2 + 9*3 = 29.
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