Find the sum of the following series 2+10+50+,,,,,,,,,,,,,+1250

The first term is $a = 2$.
To find the common ratio $r$, divide the second term by the first term:
$r = \frac{10}{2} = 5$
The last term is $L = 1250$.

The formula for the n-th term of a geometric progression is $a_n = a \cdot r^{n-1}$.
We have $a_n = 1250$, $a = 2$, and $r = 5$.

Divide both sides by 2:

We know that $5^4 = 625$.
So, $5^{n-1} = 5^4$.
Equating the exponents:

There are 5 terms in the series.

The formula for the sum of the first $n$ terms of a geometric progression is $S_n = \frac{a(r^n - 1)}{r - 1}$.
Substitute the values $a = 2$, $r = 5$, and $n = 5$:

The sum of the series is 1562.