The question is given from ncert Book of class 10th Chapter no. 5 Ex. 5.2 Q. 16. In the following question you have to find the A.P whose 3rd term is 16 and 7th term exceeds the 5th term by 12. Give the solution.
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Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.
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Solutions:
Given That,
3rd term, a3 = 16
As we all know,
a +(3−1)d = 16
a+2d = 16 ………………………………………. (i)
It is given the 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 the eq. (i),
a+2(6) = 16
a+12 = 16
a = 4
i.e The A.P. will be 4, 10, 16, 22, …