Arithmetic sequences and seriesEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

State the formula for the nth term of an arithmetic sequence.
State two formulae for the sum of the first n terms of an arithmetic series.
What is l in Sn=\frac{n}{2}(a+l)?
a=7, d=4: find u{30}.
Give the sum of the first n natural numbers.
What is \sum{r=1}^{n}q for a constant q?
How do you find the sum of terms m to n?
Outline the proof of the sum formula.
u4=17 and S{12}=324. What equations do these give?
S{10}=185, S{20}=670: find the sum of terms 11 to 20.
How can you tell an arithmetic series is decreasing?
What is the greatest sum of un=80-3n?

Exam questions on Arithmetic sequences and series

An arithmetic sequence has first term $7$ and common difference $4$ .
Find the smallest value of $n$ for which the $n$ th term is greater than $200$ .2 marks
The sum of the first $10$ terms of an arithmetic series is $185$ and the sum of the first $20$ terms is $670$ .
Find the sum of the $11$ th to the $20$ th terms inclusive.2 marks
An arithmetic series has first term $a$ and common difference $d$ .
Prove that the sum of the first $n$ terms is $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$ .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).