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Arithmetic sequence and series

In an arithmetic sequence the difference between neighbouring terms is constant. The $n$ th term is the first term plus the difference added $n - 1$ times. The sum of the first $n$ terms is the number of terms times the average of the first and the last. You therefore find the last term first, and then add. A constant difference is the sign to look for.

Try it yourself

Geometric series

a_n = a_1 + (n-1)d

term number n

S_n = \frac{n(a_1+a_n)}{2}

the sum

Symbols

$a_1$	the first term
$d$	the difference
$n$	the number of terms

Example

With $a_1 = 4$ and $d = 3$ , $a_6 = 4 + 5\cdot 3 = 19$ . The sum of the first six is $\dfrac{6(4 + 19)}{2} = 69$ .

There are

n - 1

steps from the first term to term number

n

, not

n

steps.

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Part of Mathematics R2: Sequences and series.