Arithmetic Sequences & Series (AQA A-Level Mathematics): Flashcards

Adding all terms in a sequence together

$u_n = a + (n-1)d$

Sum of first $n$ terms of a series

$S_n = \frac{n}{2}[2a + (n-1)d]$

$a$=first term, $d$=common diff, $n$=position of last term

$S_n = \frac{n}{2}[a + l]$ where $l$ is last term

Using $S_{59} - S_{21}$ (removes needed $u_{21}$)

$S_{59} - S_{20}$ to keep $u_{21}$

$q - p + 1$ (add 1 to count first term)

More efficient for algebraic work when first & last terms known