Question

Write the related series for the finite sequence –7, –10, –13, . . ., –22. Then find the sum.

Answer 1

The related series for the given sequence –7, –10, –13, . . ., –22 can be determined by finding the common difference between consecutive terms.

The common difference between each term is -3 (subtracting 3 from each term will give the next term in the sequence).

Therefore, the related series is -7, -10, -13, -16, -19, -22, ...

To find the sum of this arithmetic series, we can use the formula:
S_n = n/2 * (a_1 + a_n)

Where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the last term.

In this case, n = 6 (since there are 6 terms in the series), a_1 = -7 (the first term), and a_n = -22 (the last term).

Plugging these values into the formula, we get:
S_6 = 6/2 * (-7 + -22)
S_6 = 3 * -29
S_6 = -87

Therefore, the sum of the series –7, –10, –13, . . ., –22 is -87.