Two formulae for Sn of an arithmetic series?

\frac n2\left(2u1+(n-1)d\right) and \frac n2\left(u1+un\right)

What type of sequence does simple interest give?

Arithmetic: the same amount of interest is added each year.

Why is it n-1 in u1+(n-1)d?

There are n-1 steps from u1 to un.

What must you write if you use a GDC for a sequence?

The first term u1 and the common difference d.

Why comment on a prediction from an arithmetic model?

It may be far outside the data and the real trend may not stay constant.

How do you find n when Sn is known?

Form an equation in n, solve with the GDC, and reject any negative or non-integer value.

1.2 Arithmetic sequences and seriesIB Maths: Applications and Interpretation HL: Flashcards

Card 1 of 130 of 13 known

Question

Formula for the $n$th term of an arithmetic sequence?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

Formula for the $n$ th term of an arithmetic sequence?: $u_n=u_1+(n-1)d$
Two formulae for $S_n$ of an arithmetic series?: $\frac n2\left(2u_1+(n-1)d\right)$ and $\frac n2\left(u_1+u_n\right)$
How do you find $d$ from $u_3$ and $u_8$ ?: $d=\frac{u_8-u_3}{8-3}$
What does $\sum_{k=1}^{n}u_k$ mean?: The sum $u_1+u_2+\cdots+u_n$ .
How many terms are in $\sum_{k=a}^{b}u_k$ ?: $b-a+1$
What type of sequence does simple interest give?: Arithmetic: the same amount of interest is added each year.
A sequence is $5,9,13,\ldots$ . Find $u_{15}$ .: $5+14\times4=61$
Why is it $n-1$ in $u_1+(n-1)d$ ?: There are $n-1$ steps from $u_1$ to $u_n$ .
What must you write if you use a GDC for a sequence?: The first term $u_1$ and the common difference $d$ .
What is $d$ for $u_1=210$ and $u_5=322$ ?: $\frac{322-210}{4}=28$
Sum of the first 10 terms of $3,7,11,\ldots$ ?: $\frac{10}{2}(6+9\times4)=210$
Why comment on a prediction from an arithmetic model?: It may be far outside the data and the real trend may not stay constant.
How do you find $n$ when $S_n$ is known?: Form an equation in $n$ , solve with the GDC, and reject any negative or non-integer value.

Exam questions on 1.2 Arithmetic sequences and series

An arithmetic sequence has first term $u_1=7$ and common difference $d=4$ .
Find the value of $n$ for which $u_n=135$ .2 marks
A cyclist trains for 20 days. On day 1 she cycles 12 km, and on each following day she cycles 1.5 km further than on the previous day.
Find the first day on which she cycles more than 30 km.2 marks
An arithmetic sequence has $u_3=11$ and $u_8=31$ .
Find the common difference $d$ and the first term $u_1$ .3 marks

See the full worksheet

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).