Geometric seriesAQA A-Level Maths: Flashcards

What these 12 flashcards ask

nth term of a geometric sequence?
Sum of the first n terms of a geometric series?
Sum to infinity?
Condition for a geometric series to converge?
What does |r|<1 mean?
How do you find the common ratio?
u2=12 and u5=1.5: find r.
a=2, r=3: the 5th term?
a=40, r=0.6: S\infty?
What is S\infty-Sn?
How do you solve for n in ar^n= a number?
Sum of the terms from the kth onwards?

Exam questions on Geometric series

A geometric sequence has first term $2$ and common ratio $3$ .
Find the least value of $n$ for which the sum of the first $n$ terms exceeds $10^6$ .2 marks
A geometric series has first term $40$ and common ratio $0.6$ .
Find the least value of $n$ for which $S_\infty-S_n<0.001$ .2 marks
A geometric series has second term $12$ and fifth term $1.5$ .
Find the common ratio and the first term.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).