In an arithmetic sequence, the 3rd term is 10 and the 7th term is 26. What is the 10th term?
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Correct answer
A. 38
Principle or equation
For an arithmetic sequence, the nth term is given by a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference. Use given terms to solve for a_1 and d.
Why this answer is correct
Let a_3 = a_1 + 2d = 10 and a_7 = a_1 + 6d = 26. Subtracting gives 4d = 16, so d = 4. Then a_1 + 8 = 10 ⇒ a_1 = 2. Then a_10 = a_1 + 9d = 2 + 36 = 38.
Example
If a_2 = 5 and a_5 = 14, then d = (14-5)/3 = 3, a_1 = 2, so a_10 = 2 + 9*3 = 29.
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