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7. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

7. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
Given that, 11th term, a11 = 38 and 16th term, a16 = 73 We know that, an = a+(n−1)d a11 = a+(11−1)d 38 = a+10d ………………………………. (i) In the same way, a16 = a +(16−1)d 73 = a+15d ………………………………………… (ii) On subtracting equation (i) from (ii), we get 35 = 5d d = 7 From equation (i), we can write, 38 = a+10×(7) 38 − 70 = a a = −32 a31 = a +(31−1) d = − 32 + 30 (7) = − 32 + 210 = 178 Hence, 31st term is 178.

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