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In an AP(v) Given d = 5, S9 = 75, find a and a9. Q.3(5)

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The best way to solve this hard question of chapter arithmetic progressions of exercise 5.3 of math . What is the easy solution In an AP(v) Given d = 5, S9 = 75, find a and a9.

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  1. Given that, d = 5, S9 = 75

    As, sum of n terms in AP is,

    Sn = n/2 [2a +(n -1)d]

    Therefore, the sum of first nine terms are;

    S9 = 9/2 [2a +(9-1)5]

    25 = 3(a+20)

    25 = 3a+60

    3a = 25−60

    a = -35/3

    As we know, the nth term can be written as;

    an = a+(n−1)d

    a9 = a+(9−1)(5)

    = -35/3+8(5)

    = -35/3+40

    = (35+120/3) = 85/3

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