What is the 32nd term of the arithmetic sequence where a1 = −33 and a9 = −121? −396 −385 −374 −363

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What is the 32nd term of the arithmetic sequence where a1 = −33 and a9 = −121? −396 −385 −374 −363

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  1. Ava
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    2021-09-14T19:24:30+00:00

    The formula to find the general term of an arithmetic sequence is,

     a_{n} =a_{1} +(n-1)d

    Where  a_{n}  = nth term and

     a_{1} = First term.

    Given, a9 = −121. Therefore, we can set up an equation as following:

     -33+(9-1)d = -121 Since, a1 = -33

    – 33 + 8d = -121

    -33 + 8d + 33 = -121 + 33 Add 33 to each sides of the equation.

    8d = -88.

     \frac{8d}{8} =\frac{-88}{8}  Divide each sides by 8.

    So, d = – 11.

    Now to find the 32nd terms, plug in n = 32, a1 = -33 and d = -11 in the above formula. So,

     a_{32} = -33 +(32 -1) (-11)

    = -33 + 31 ( -11)

    = – 33 – 341

    = -374

    So, 32nd term = – 374.

    Hope this helps you!

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