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Reviewed CSCA Mathematics question · Hard

In an arithmetic sequence, the 3rd term is 14 and the 9th term is 38. What is the 15th term?

  1. 62
  2. 60
  3. 58
  4. 56
Show the answer and explanation

Correct answer

A. 62

Principle or equation

For an arithmetic sequence, the nth term is a_n = a_1 + (n - 1)d. Use the given terms to find the common difference d and the first term a_1.

Why this answer is correct

a_3 = a_1 + 2d = 14, a_9 = a_1 + 8d = 38. Subtract: 6d = 24 → d = 4. Then a_1 = 14 - 2*4 = 6. So a_15 = 6 + 14*4 = 62.

Example

If a_2=9 and a_6=25, then d=4, a_1=5, a_10=41.

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