# Test: Geometric Series I - Normal

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Question 1:   The fifth term of the geometric progression is  ${a}_{5}=9$ ,  and common ratio is  $r=-3$ .  Find the sixth  $\left({a}_{6}\right)$  term of the progression.
$6$
$-27$
$-\frac{1}{3}$
$-3$
Question 2:   In the geometric progression  $\left({a}_{n}\right)$ ,  the initial term is  ${a}_{1}=16$ ,  and the common ratio is  $r=-\frac{1}{2}$ .  Find the fifth term of the sequence.
$-1$
$-8$
$8$
$1$
Question 3:   Find the common ratio and the fifth term of the geometric sequence:  $\frac{1}{216}$ ,$\frac{1}{36}$ ,$\frac{1}{6}$ ….
${a}_{5}=216$  and  $r=6$
${a}_{5}=6$  and  $r=6$
${a}_{5}=-1$  and  $r=-6$
${a}_{5}=1$  and  $r=-6$
Question 4:   Find the common ratio  $\left(r\right)$  of the geometric sequence  $\left({a}_{n}\right)$  if  ${a}_{1}=2$  and  ${a}_{5}=32$ .
$-2$
$-\frac{1}{2}$
$2$
$\frac{1}{2}$
Question 5:   Find third term of geometric progression if  ${a}_{2}=25$  and  ${a}_{4}=49$ .
$37$
$14$
$\frac{49}{25}$
$35$
Question 6:   For any natural  $n$ ,  the sum of the first  $n$  terms of the geometric progression  $\left({a}_{n}\right)$  is  ${S}_{n}=5\left({3}^{n}-1\right)$ .  Find the initial term and the common ratio  $\left(r\right)$ .
${a}_{1}=10$  and  $r=4$
${a}_{1}=0$  and  $r=4$
${a}_{1}=10$  and  $r=3$
${a}_{1}=0$  and  $r=3$
Question 7:   Find the sum of  $n$  first terms of the geometric progression  $\left({a}_{n}\right)$  if  ${a}_{1}=-8$ ,  $r=\frac{1}{2}$  and  $n=4$ .
$-14$
$14$
$15$
$-15$
Question 8:   Find the sum of the first five terms of the geometric progression  $\left({a}_{n}\right)$ :  $12,36,108...$
$2904$
$324$
$1452$
$726$
Question 9:   Find the sum of the infinite geometric progression  $\left({a}_{n}\right)$  if  ${a}_{1}=55$  and  $r=\frac{1}{6}$ .
$48$
$56.5$
$330$
$66$
Question 10:   Find the sum of the infinite geometric sequence:  $10,\text{}\text{}1,\text{}\text{}0.1$
$100$
$0.01$
$\frac{9}{100}$
$\frac{100}{9}$