vi) given a=2, d=8, S = 90, find n and an​

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vi) given a=2, d=8, S = 90, find n and an​

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Liliana 3 weeks 2021-10-07T13:11:57+00:00 2 Answers 0 views 0

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    2021-10-07T13:13:11+00:00

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    hunk537

    hunk537

    03.03.2017

    Math

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    In an Ap given , a=2 , d=8 , sn = 90 . find n and an

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    Sn = 90

    Sn = n/2 [ 2a + (n – 1)d]

    90 = n/2 [ 2 x 2 + (n – 1)8]

    180/n = 4 + 8n – 8

    180/n = 8n – 4

    180 = 8n^2 – 4n

    8n^2 – 4n – 180 = 0

    2n^2 – n – 45 = 0

    2n^2 – 10n + 9n – 45 = 0

    2n( n – 5) + 9( n – 5) = 0

    (2n + 9)(n – 5) = 0

    n = -9/2 or n = 5

    But n cannot be negative.

    So, n = 5

    an = a + (n – 1)d

    a5 = 2 + (5-1)8

    a5 = 2 + 4 x 8

    a5 = 2 + 32 = 34

    0
    2021-10-07T13:13:22+00:00

    Answer:

    a=2,d=8,s

    n

    =90

    s

    n

    =

    2

    n

    [2a+(n−1)d]

    90=

    2

    n

    [4+(n−1)8]

    180=n[8n−4]

    180=8n

    2

    −4n

    =8n

    2

    −4n−180=0

    =2n

    2

    −n−45=0

    =2n

    2

    −10n+9n−45=0

    =2n(n−5)−9(n−5)

    =(2n−9)(n−5)

    n=5

    a

    n

    =a+(n−1)d

    a

    n

    =2+(5−1)8

    a

    n

    =2+32

    a

    n

    =34

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