Sum of the first n terms (using a and d)?

Sn=\frac n2\left[2a+(n-1)d\right]

Outline the proof of the sum formula.

Write the sum forwards and backwards, add to get n pairs each equal to 2a+(n-1)d, then halve.

How do you find the smallest n with Sn above a target?

Form a quadratic inequality, solve it, then check the integers either side.

Arithmetic sequences and seriesEdexcel International A Level Maths: Flashcards

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$n$th term of an arithmetic sequence?

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$n$ th term of an arithmetic sequence?: $u_n=a+(n-1)d$
Sum of the first $n$ terms (using $a$ and $d$ )?: $S_n=\frac n2\left[2a+(n-1)d\right]$
Sum of the first $n$ terms (using the last term $l$ )?: $S_n=\frac n2(a+l)$
Sum of the first $n$ natural numbers?: $\frac{n(n+1)}{2}$
What does $\displaystyle\sum_{r=1}^{n}u_r$ mean?: $u_1+u_2+\dots+u_n$
What is $\displaystyle\sum_{r=1}^{n}c$ for a constant $c$ ?: $nc$
How do you find $\displaystyle\sum_{r=11}^{20}u_r$ ?: $S_{20}-S_{10}$
How many terms in $\displaystyle\sum_{r=5}^{12}$ ?: $12-5+1=8$
Outline the proof of the sum formula.: Write the sum forwards and backwards, add to get $n$ pairs each equal to $2a+(n-1)d$ , then halve.
$a=7$ , $d=4$ . Find $u_{20}$ .: $7+19\times4=83$
$u_3=11$ , $u_8=36$ . Find $d$ .: $5d=25$ , so $d=5$ .
How do you find the smallest $n$ with $S_n$ above a target?: Form a quadratic inequality, solve it, then check the integers either side.

Exam questions on Arithmetic sequences and series

The first term of an arithmetic sequence is $7$ and the common difference is $4$ .
Find the smallest value of $n$ for which the $n$ th term is greater than $200$ .2 marks
A sequence has $r$ th term $u_r=3r+1$ .
Find the value of $\displaystyle\sum_{r=11}^{20}u_r$ .2 marks
An arithmetic series has third term $11$ and eighth term $36$ . The sum of the first $n$ terms is $S_n$ .
Find the first term and the common difference.3 marks

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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).