IB Maths AA SL 1.8 Infinite geometric series Question Bank

Practise IB Maths AA SL 1.8 by finding common ratios, convergence conditions and sums to infinity in geometric sequences.

Exam points

Identify the common ratio and decide whether an infinite geometric series converges.
Use the sum-to-infinity formula to find an unknown term, ratio or parameter.
Interpret convergence in an applied context such as deposits, repeated lengths or target values.

[Maximum number: 7]

(a)

Consider an infinite geometric sequence with $u_{1}=40$ and $r=\frac{1}{2}$ .

[ 2 ]

(i)

Find the sum of the infinite sequence.

[ 2 ]

correct substitution into formula for infinite sum
e.g. $S_{\infty}=\frac{40}{1-0.5}, S_{\infty}=\frac{40}{0.5}$

S_{\infty}=80

(b)

The sum of the infinite geometric sequence is equal to twice the sum of the arithmetic sequence. Find n.

[ 5 ]

multiplying $S_{n}$ (AP) by 2 or dividing S (infinite GP) by 2
e.g. $2 S_{n}, \frac{S_{\infty}}{2}, 40$
evidence of substituting into $2 S_{n}=S_{\infty}$
e.g. $2 n^{2}-38 n=40,4 n^{2}-76 n-80(=0)$
attempt to solve their quadratic (equation)
e.g. intersection of graphs, formula

n=20

9. Note: There may be slight differences in answers, depending on whether candidates use tables or GDCs, or their 3 sf answers in subsequent parts. Do not penalise answers that are consistent with their working and check carefully for FT.

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SL 1.8—Infinite geometric series question 1

Question (a)

Question (i)

Question (b)