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4.05 Geometric series

Interactive practice questions

Consider the series $8+1+\frac{1}{8}$8+1+18$\dots$

Find the sum of the first $7$7 terms. Round your answer to three decimal places if necessary.

Easy
2min

Consider the series $1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\text{. . .}+\frac{1}{1024}$112+1418+. . .+11024.

Which of the following expresses the series in the form $\sum_{k=1}^{\editable{}}\editable{}$k=1?

 

Medium
3min

Consider the series $1+2+4$1+2+4 ...

Find the sum of the first $10$10 terms.

Easy
1min

Find the sum of the first $5$5 terms of the geometric sequence defined by $t_1=5.723$t1=5.723 and $r=1.921$r=1.921.

Give your answer correct to two decimal places.

Easy
1min
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Outcomes

1.5.1.4

establish and use the formula S_n=t_1 (r^n−1)/(r−1) for the sum of the first n terms of a geometric sequence

1.5.1.6

use geometric sequences in contexts involving geometric growth or decay, including compound interest and annuities

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