Find the sum of the GP 2+10+50.......+250
To find the sum of a geometric progression (GP), we will use the formula:
Sum of GP = a(r^n - 1) / (r - 1)
where:
a = first term of the GP = 2
r = common ratio = 5 (50/10 = 5)
n = number of terms = n
We need to find the value of n first:
2 * 5^(n-1) = 250
5^(n-1) = 125
n - 1 = 3
n = 4
Now we can find the sum of the GP:
Sum = 2 * (5^4 - 1) / (5 - 1)
Sum = 2 * (625 - 1) / 4
Sum = 2 * 624 / 4
Sum = 1248
Therefore, the sum of the GP 2, 10, 50, ..., 250 is 1248.