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8 January, 12:58

Find the first 3 terms of the arithmetic series given aq=17, an=197, Sn=2247.

(*Hint: you may have to use both formulas)

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  1. 8 January, 13:19
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    Arithmetic Series

    First three terms are 17,26 and 35

    Step-by-step explanation:

    Let the common difference of this AP be b

    Given 1st term of the arithmetic series is a1=17,

    Then the nth term of the arithmetic progression is an = a + (n-1) * b=197,

    The sum of the Arithmetic progression is Sn = 2247

    And total number of terms is n.

    And we know that the formula of sum of an AP is

    S = (n/2) * (2*a + (n-1) * b)

    ⇒ S = (n/2) * (a + a + (n-1) * b)

    ⇒2247 = (n/2) * (17 + 197)

    therefore, n/2 = 2247 / (214) = 21

    and hence the value of n from the equation is 21

    and we also know that

    an = a + (n-1) * b

    ⇒ 197=17 + (21-1) * b

    ⇒ 197-17 = 20 * b

    ⇒ 180/20 = b

    And thus the value of b is 9

    So the first three terms of the arithmetic progression is

    The first term, A1 = 17

    The second term, A2 = a1 + b

    = 17 + 9

    = 26

    The third term, A3 = a2+b

    =26 + 9

    =35

    Hence First three terms are 17,26 and 35
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