The 6th term of an AP is – 10 and 10th term is -26. Determine the sum of the first 20 terms of the AP .

Question

The 6th term of an AP is – 10 and 10th term is -26. Determine the sum of the first 20 terms of the AP .

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Elliana 2 weeks 2021-10-14T11:44:56+00:00 2 Answers 0 views 0

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    0
    2021-10-14T11:46:10+00:00

    \huge{\mathcal{\underline{\green{SOLUTION}}}}

    Let a be the First term of the AP

    Common Difference = d

     {6}^{th}  \: term \:  = a_6 = a + (6 - 1)d \:  = a + 5d

    {10}^{th}  \: term \:  = a_{10} = a + (10- 1)d \:  = a + 9d

    So

    a \:  + 5d \:  =  - 10...........(1)

    a \:  + 9d \:  =  - 26...........(2)

    Now Equation (1) Equation (2) gives

     - 4d \:  = 16

     \implies \: d \:  =  - 4

    From Equation (1)

    a \:  = 20 - 10 = 10

    Hence the sum of first 20 terms

    S_{20} =  \frac{20}{2} (2a \:  + 19d)

     = 10 \times (2 \times 10 + 19 \times ( - 4))

     = 10 \times (20 - 76)

     =  - 560

    \displaystyle\textcolor{red}{Please \:  Mark \:  it  \: Brainliest}

    0
    2021-10-14T11:46:26+00:00

    Answer:

    -560 is answer dear friend

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