Multiple choice

What is the tenth term of the arithmetic sequence whose first term is $x$ and whose third term is $x + 6a$?

  1. $33a$
  2. $x + 24a$
  3. $x + 27a$
  4. $x + 30a$
  5. $x + 33a$
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C Correct answer
Explanation

Arithmetic sequence: a1 = x, a3 = x + 2d = x + 6a. Thus 2d = 6a, d = 3a. The 10th term is a1 + 9d = x + 9(3a) = x + 27a.

AI explanation

The difference between the first term and the third term is 6a, meaning two common steps equal 6a, so the common difference is 3a. The nth term of an arithmetic sequence is given by a + (n-1)d. Therefore, the tenth term is x + 9 times 3a, which equals x + 27a.

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