# Test: Geometric Series - Ambitious

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Question 1:   Which of the following are geometric series?
$4,8,16...$
$3,6,10...$
$4,8,12...$
$-\frac{1}{2},\frac{1}{2},-\frac{3}{2}...$
Question 2:   Which of the following are geometric series?
$\frac{1}{2},\frac{1}{4},-\frac{1}{9}$.
$1.5,1,0.5...$
$2,-4,-9...$
$9,-3,1...$
Question 3:   Find a common ratio in the following geometric series: $5,15,45...$
$r=5$
$r=3$
$r=-3$
$r=\frac{1}{3}$
Question 4:   Find the $14$th term in the following geometric series: $12,6,3...$
${a}_{14}\approx 0.0031$
${a}_{14}\approx 0.15$
${a}_{14}\approx 0.0172$
${a}_{14}\approx 0.00146$
Question 5:   Find the sum of the first $5$ terms in the following series: $3\frac{1}{2},7,14,...$
${S}_{5}=98.5$
${S}_{5}=108.5$
${S}_{5}=98$
${S}_{5}=102.5$
Question 6:   Find the sum of first $14$ terms in the following series: $1,\frac{1}{4},\frac{1}{16},...$
${S}_{6}\approx 1.29$
${S}_{6}\approx 1.33$
${S}_{6}\approx 1.5$
${S}_{6}\approx 1.66$
Question 7:   Find the sum to infinity of the following series: ${5}_{,}\frac{5}{3},\frac{5}{9},...$
${S}_{\infty }=10$
${S}_{\infty }=7\frac{1}{2}$
${S}_{\infty }=5$
${S}_{\infty }=8\frac{2}{3}$
Question 8:   Find the sum to infinity of the following series: $7,-\frac{14}{5},\frac{28}{25},...$
${S}_{\infty }=6\frac{7}{8}$
${S}_{\infty }=5$
${S}_{\infty }=5\frac{9}{10}$
${S}_{\infty }=4\frac{1}{2}$
Question 9:   Find the range of values where the following series has a sum to infinity. $1-\frac{2x}{3}+\frac{4{x}^{2}}{3}-\frac{8{x}^{3}}{27}+...$
$-\frac{3}{2}
$-1
$-\frac{1}{2}
$-\frac{2}{3}
Question 10:   What is the least number of terms in the geometric series $1,3,9,...$, if the sum exceeds $1000$?
$n=6$
$n=9$
$n=8$
$n=7$