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8.05 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

Use the sequence facility of your calculator to determine for which term number $n$n the geometric sequence $T_n=6\left(2.1^{n-1}\right)$Tn=6(2.1n1) has a sum of $217.3146$217.3146.

Medium
2min

Use the sequence facility of your calculator to determine for which term number $n$n the geometric sequence $T_n=800\left(0.9^{n-1}\right)$Tn=800(0.9n1) has a sum of $4556.26232$4556.26232.

Medium
1min

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

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

Easy
1min
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Outcomes

ACMMM075

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

ACMMM076

use geometric sequences in contexts involving geometric growth or decay, such as compound interest

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