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Deepak Bora
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An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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The question is given from NCERT Book of class 10th Ch. no. 5 Ex. 5.2 Q. 8. In the following question you have to find the 29th term of an A.P which has 50 terms in which 3rd term is 12 and last term is 106. Give the answer briefly.

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  1. Solution: 

    3rd term, a3 = 12

    50th term, a50 = 106

    We know,

    an = a + (n−1)d

    a3 = a + (3−1)d

    12 = a + 2d ……………………………. (i)

    Like above,

    a50 a+(50−1)d

    106 = a+49d …………………………. (ii)

    By subtracting (i) from (ii),

    94 = 47d

    d = 2 = common difference

    From equation (i),

    12 = a + 2(2)

    a = 12 − 4 = 8

    a29 = a + (29−1) d

    a29 = 8 + (28)2

    a29 = 8 + 56 = 64

    The 29th term is 64.

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