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

, a_{3}= 16As we all know,

a+(3−1)d= 16a+2d= 16 ………………………………………. (i)It is given the 7th term exceeds the 5th term by 12.

a_{7}−a_{5}= 12[

a+(7−1)d]−[a+(5−1)d]= 12(

a+6d)−(a+4d) = 122

d= 12d= 6From the eq. (i),

a+2(6) = 16a+12 = 16a= 4i.e The A.P. will be 4, 10, 16, 22, …