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

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

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
2 months ago
Given that, 3rd term, a3 = 12 50th term, a50 = 106 We know that, an = a+(n−1)d a3 = a+(3−1)d 12 = a+2d ……………………………. (i) In the same way, a50 = a+(50−1)d 106 = a+49d …………………………. (ii) On subtracting equation (i) from (ii), we get 94 = 47d d = 2 = common difference From equation (i), we can write now, 12 = a+2(2) a = 12−4 = 8 a29 = a+(29−1) d a29 = 8+(28)2 a29 = 8+56 = 64 Therefore, 29th term is 64.

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