# 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.
$6$
$-27$
$-3$
$-\frac{1}{3}$
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.
$-1$
$1$
$-8$
$8$
Question 3:   Find the common ratio and the fifth term of the geometric sequence:  $\frac{1}{216}$ ,$\frac{1}{36}$ ,$\frac{1}{6}$ ….
${a}_{5}=6$  and  $r=6$
${a}_{5}=216$  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  ${a}_{5}=32$ .
$\frac{1}{2}$
$-\frac{1}{2}$
$-2$
$2$
Question 5:   Find third term of geometric progression if  ${a}_{2}=25$  and  ${a}_{4}=49$ .
$\frac{49}{25}$
$37$
$35$
$14$
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