In an arithmetic sequence, the 5th term is 17 and the 9th term is 29. What is the 20th term?
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Correct answer
B. 58
Principle or equation
For an arithmetic sequence, the nth term is a_n = a_1 + (n-1)d. Use given terms to find a_1 and d.
Why this answer is correct
Let a_5 = a_1 + 4d = 17 and a_9 = a_1 + 8d = 29. Subtract: 4d = 12 => d = 3. Then a_1 = 17 - 4*3 = 5. Then a_20 = 5 + 19*3 = 62.
Example
If a_3 = 10 and a_7 = 22, then d = 3, a_1 = 4, so a_10 = 31.
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