PrepZii

formula

Arithmetic Progression: Term and Sum

The source defines an A.P. using first term $a$ and common difference $d$ .

a,\ a+d,\ a+2d,\ldots,\ a+(n-1)d

t_n=a+(n-1)d

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

t_r=S_r-S_{r-1}

$a$

constant, endpoint, or first term

$d$

common difference

$n$

positive integer or index