# Consider the following series: 50 + -10 + 2 + ... what is the sum of the first 5 terms?

$\frac{1024}{25}$ or $41.68$
This series looks like a geometric progression(GP) with a common ratio of $- \frac{1}{5}$. A geometric progression is a series of the form $a , a \cdot r , a \cdot {r}^{2} , \ldots$ where ‘r’ is called the common ratio.The formula for the sum of a geometric series is $a \cdot \frac{{r}^{n} - 1}{r - 1}$ where ‘a’ is the first term, ‘r’ is the common ratio and ‘n’ is the number of terms. Substituting the values from the given series, we get 50*(((-1/5)^5)-1)/((-1/5)-1
This simplifies into $\frac{1024}{25}$ or 41.68