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Bot GPT 3.5 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.