Geometric sequences and seriesEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

State the nth term of a geometric sequence.
State the sum of the first n terms of a geometric series.
State the sum to infinity and the condition for it to exist.
What does |r|<1 mean?
How do you find r from two terms of a geometric sequence?
Outline the proof of the sum formula.
a=64, r=\frac34: find S\infty.
a=4, r=3: find S8.
What happens to the signs if r<0?
Why does dividing by \ln r reverse an inequality when 0<r<1?
What is the sum of the terms from the mth onwards when |r|<1?
For which x does 1+3x+9x^2+\cdots converge?

Exam questions on Geometric sequences and series

A geometric sequence has first term $64$ and common ratio $\frac34$ .
Find the least value of $n$ for which the $n$ th term is less than $1$ .2 marks
A geometric series has second term $12$ and fifth term $324$ .
Find the sum of the first $8$ terms.2 marks
A geometric series has first term $a$ and common ratio $r$ , where $r\ne1$ .
Prove that the sum of the first $n$ terms is $S_n=\frac{a(1-r^n)}{1-r}$ .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).