in any series the term of n is 3-2 n. so find sum of n term​

Question

in any series the term of n is 3-2 n. so find sum of n term​

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Sarah 3 weeks 2021-08-23T06:08:37+00:00 1 Answer 0 views 0

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    2021-08-23T06:10:08+00:00

    Answer:

    First term (a) = 3 – 2×(1) = 1

    a2 = 3 – 2×(2) = -1

    a3 = 3 – 2×(3) = -3

    As the difference between a3,a2 and a2,a1 is same so the series is in AP

    common difference (d)= -1 – 1 = -2

    sum \:  =  \frac{n}{2} (2a + (n - 1)d) \\  =  \frac{n}{2} (2 + (n - 1)( - 2)) \\  =  \frac{n}{2} (2  - 2n + 2) \\  =  \frac{n}{2} (4 - 2n) \\  = n(2 - n) \\  = 2n -  {n}^{2}

    which is the required ans

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