Find the sum of the first 40 terms of the arithmetic sequence 17, 24, 31,

The sum of the first 40 terms of 17, 24, 31, 38,..., with a common difference of 7 is: 6,140.

Recall:

Thus, the first term of the sequence, 17, 24, 31, 38,..., is: 17

Common difference (d) = 38 - 31 = 31 - 24 = 24 - 17 = 7

Plug in the values into the formula for finding the sum of the first n terms:

Therefore, the sum of the first 40 terms of 17, 24, 31, 38,..., with a common difference of 7 is: 6,140.

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6120

Step-by-step explanation:

First let's calculate the 40th term.  Here a(n) = 17+7(n-1), so a(40) = 17 + 7(39).  This works out to 290.

To find the sum of the first 40 terms, add together the first and last terms and then divide the result by 2 (which gives us the average of the first and last terms), and then mult. this result by 40, the number of terms:

40(17 + 290)/2 = 40(306)/2 = 6120

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