Number of bugs on 1st day = 35
Number of bugs on 1st 2nd day = 52
Number of bugs on 3rd day = 69
35,52,69,....
From the above sequence it is clear that the common difference 17 which is constant.
So the given sequence is in AP
Formula for nth term is
a(n)= a1 + (n-1) *d
n = number of terms = 15
d= common difference = 17
a1 = first term = 35
So a(15) = 35 + (15-1)*17
a(15) = 35 + 14(17)
a(15) = 35 + 238
a(15) = 273
So number of bugs on 15th day is 273
