Question

The sum of the geometric series is

• A. $S=a+ar+a{r}^2+a{r}^3+...+a{r}^n$
• B. $S=a-ar+a{r}^2+a{r}^3+...+a{r}^n$
• C. $S=a+ar-a{r}^2+a{r}^3-...+a{r}^n$
• D. $S=a-ar-a{r}^2-a{r}^3+...-a{r}^n$

Answer 1

The correct option is A $S=a+ar+a{r}^2+a{r}^3+...+a{r}^n$

We have $n$ is the number of terms, $a$ is the first term and $r$ is the common ratio. Thus the sum of first $n$ terms of a geometric sequence is called geometric series.

Here geometric series is $a,ar,a{r}^2,a{r}^3,...........a{r}^n$

Thus sum $S=a+ar+a{r}^2+a{r}^3+...........+a{r}^n$