Multiple choice

In an arithmetic sequence, the sum of the first 20 terms is 670, and the first term is 5. Find the common difference.

  1. 3

  2. 4

  3. 5

  4. 6

  5. 7
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A Correct answer
Explanation

Sum of arithmetic series S = n/2 * (2a + (n-1)d). 670 = 20/2 * (2*5 + 19d). 670 = 10 * (10 + 19d). 67 = 10 + 19d. 57 = 19d. d = 3.

AI explanation

The sum of an arithmetic sequence is given by S = n/2 * [2a + (n - 1)d], where a is the first term and d is the common difference. Substituting the known values gives 670 = 20/2 * [2(5) + 19d], which simplifies to 67 = 10 + 19d. Solving this equation yields a common difference of 3.

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