To find the number of terms needed in the geometric progression (GP) so that the sum exceeds 35, we can use the formula for the sum of the first n terms of a geometric progression:
S_n = a * (1 - r^n) / (1 - r)
Where: S_n = sum of the first n terms a = first term of the GP r = common ratio of the GP n = number of terms
In this case, the first term (a) is 4 and the common ratio (r) is 3.6 / 4 = 0.9.
We want to find the number of terms (n) needed so that the sum exceeds 35: