A carpenter

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,………………………………

⇒ S_n = 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