In an arithmetic sequence, the 6th term is 23 and the 10th term is 35. What is the 15th term?
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Correct answer
A. 50
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.
Why this answer is correct
Let a_1 be the first term and d the common difference. Then a_6 = a_1 + 5d = 23 and a_10 = a_1 + 9d = 35. Subtracting gives 4d = 12, so d = 3. Then a_1 = 23 - 5*3 = 8. Thus a_15 = 8 + 14*3 = 50.
Example
For an arithmetic sequence with a_3 = 10 and a_7 = 26, d = (26-10)/(7-3) = 4, a_1 = 10 - 2*4 = 2, so a_10 = 2 + 9*4 = 38.
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