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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    2021-09-09T20:39:57+00:00

    The Given Sequence is an Arithmetic Sequence with First term = -19

    ⇒ a = -19

    Second term is -13

    We know that Common difference is Difference of second term and first term.

    ⇒ Common Difference (d) = -13 + 19 = 6

    We know that Sum of n terms is given by : S_n = \frac{n}{2}(2a + (n - 1)d)

    Given n = 63 and we found a = -19 and d = 6

    \implies S_6_3 = \frac{63}{2}(2(-19) + (63 - 1)6)

    \implies S_6_3 = \frac{63}{2}(-38 + (62)6)

    \implies S_6_3 = \frac{63}{2}(-38 + 372)

    \implies S_6_3 = \frac{63}{2}(-38 + 372)

    \implies S_6_3 = \frac{63}{2}(334)

    \implies S_6_3 = {63}(167) = 10521

    The Sum of First 63 terms is 10521

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