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16. Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.

16. Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
Given, Third term, a3 = 16 As we know, a +(3−1)d = 16 a+2d = 16 ………………………………………. (i) It is given that, 7th term exceeds the 5th term by 12. a7 − a5 = 12 [a+(7−1)d]−[a +(5−1)d]= 12 (a+6d)−(a+4d) = 12 2d = 12 d = 6 From equation (i), we get, a+2(6) = 16 a+12 = 16 a = 4 Therefore, A.P. will be4, 10, 16, 22, …

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