1.11 Sum of infinite geometric sequencesIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

Formula for un of a geometric sequence?
Formula for Sn of a geometric sequence?
Formula for the sum to infinity?
Condition for S\infty to exist?
What happens to r^{n} if |r|<1?
What is a convergent series?
u1=12, r=\frac13: find S\infty.
u1=5, S\infty=20: find r.
Write 0.272727\ldots as a fraction.
Ball dropped from 2 m rises to 80\% each time: total distance?
Why is the bounce total not just \frac{u1}{1-r}?
What is the sum to infinity of 8+4+2+\ldots?

Exam questions on 1.11 Sum of infinite geometric sequences

A geometric sequence has first term $u_1=12$ and common ratio $r=\frac13$ .
Use your GDC to find the least value of $n$ for which the sum of the first $n$ terms is greater than $17.9$ .2 marks
A ball is dropped from a height of $2$ m onto a hard floor. After each bounce it rises to $80\%$ of the height from which it last fell.
Use your GDC to find the number of the first bounce after which the ball rises to less than $0.1$ m.2 marks
The recurring decimal $0.272727\ldots$ can be written as the sum of an infinite geometric series.
Write down the first term and the common ratio of the series $0.27+0.0027+0.000027+\ldots$ , and explain why its sum to infinity exists.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).