Find the sum of the first 63 terms of –19, -13, -7 …

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Find the sum of the first 63 terms of –19, -13, -7 …

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    2021-09-09T20:44:16+00:00

    You can tell this is an arithmetic sequence because it is a list of terms beginning with -19 that increase by 6 each term. Because of this, we can use the formula for the sum of an arithmetic sequence, which is:

    S = \dfrac{n}{2}[2 a_1 + d(n - 1)]

    • n is the number of terms in the sequence
    • a_1 is the starting term
    • d is the common difference among the terms

    In this case, we can see that n = 63, a_1 = -19, and d = 6. Thus, we can use the formula:

    S = \dfrac{63}{2} [2(-19) + 6(62)] = 10,521

    Our answer is 10,521.

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