Answer :

Given: Carpenter was hired to build 192 frames. He made 5 frames on first day and two more frames for every next day


To find: Number of days taken by him to build 192 frames


According to question:


A.P. will be 5, 7, 9,………………………………


Sn = 192, a = 5 and d = 7 – 5 = 2


Formula used:



where a is first term, d is common difference and n is number of terms in an A.P.


Therefore,








n2 + 16n – 12n + 192 = 0


n(n + 16) – 12(n + 16) = 0


(n + 16)(n – 12) = 0


n = –16 or 12


n is number of days and it cannot be negative


Therefore, we will take value of n = 12


Hence, he will take 12 days to build 192 frames


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