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Question

The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.

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Solution

We have: S7 = 10722a+(7-1)d = 10722a+6d =10a+3d = 107 ...(i)Also, the sum of the next seven terms = S14 - S7 = 171422a+14-1d-722a+(7-1)d = 1772a+13d-722a+6d =1714a+91d - 7a-21d = 177a+70d = 17a+10d = 177 ...(ii)From (i) and (ii), we get:107 -3d = 177-10d7d= 1d = 17Putting the value in (i), we get:a+3d = 107a+37 = 107a = 1 a = 1, d = 17
The progression thus formed is 1, 87, 97, 107...

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