A geometric sequence is given by the general form:
[tex]a_n=a\cdot r^{n-1}[/tex]Where a is the first term of the sequence and r is known as the common ratio. If the common ratio is smaller than one then the sum of all the elements is equal to:
[tex]\sum ^{\infty}_{n\mathop=1}a\cdot r^{n-1}^{}=\frac{a}{1-r}[/tex]So as I stated before this expression can only be used if r<1. From the four options given by the exercise the only one with r<1 us the first one. Then the answer is the first option.
