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Reviewed CSCA Mathematics question · Easy

In an arithmetic sequence, the 2nd term is 9 and the 6th term is 25. What is the 10th term?

  1. 37
  2. 41
  3. 45
  4. 49
Show the answer and explanation

Correct answer

C. 45

Principle or equation

For an arithmetic sequence, a_n = a_1 + (n-1)d. Use given terms to find d and a_1, then compute a_10.

Why this answer is correct

Let a_2 = a_1 + d = 9, a_6 = a_1 + 5d = 25. Subtract: 4d = 16, so d = 4. Then a_1 = 9 - 4 = 5. Thus a_10 = 5 + 9*4 = 41.

Example

If a_3 = 10 and a_7 = 22, then 4d = 12, d=3, a_1 = 10 - 2*3 = 4, so a_10 = 4 + 9*3 = 31.

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