Find the sum of the GP 2+10+80.......+250
To find the sum of this geometric progression (GP), we can first identify the common ratio (r) between each term.
The common ratio can be found by dividing the second term by the first term:
r = 10/2 = 5
Now, we can use the formula for the sum of a geometric progression to find the sum of the given series.
Sum of a GP = a*(r^n - 1) / (r - 1)
Where:
a = first term = 2
r = common ratio = 5
n = number of terms
To find the number of terms in the series, we can use the formula:
nth term = a*(r^(n-1))
250 = 2*(5^(n-1))
125 = 5^(n-1)
n-1 = 3
n = 4
Now, plug in the values into the sum formula:
Sum = 2*(5^4 - 1) / (5 - 1)
Sum = 2*(625 - 1) / 4
Sum = 2 * 624 / 4
Sum = 1248
Therefore, the sum of the given geometric progression is 1248.