Arithmetic Progression (AP)

Arithmetic progression is a sequence of numbers such that the difference between each consecutive term is constant, commonly denoted by $d$. For example:

$3, 5, 7, 9, ...$

Here, the first term, $a$, is $3$, $a=3$, and the common difference, $d$, is $2$, $d=2$. In general, AP is

$a, a+d , a+2d, ... , a+(n-1)d$

where $nth$ term $a_{n} = a+(n-1)d$

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Sum

Sum of AP with $n$ terms is

$a + (a+d) + (a+2d) + ... + (a+(n-1)d)$

= $na + d(1 + 2 + 3 + ... + n-1)$

= $na + d(\frac{n(n-1)}{2})$

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

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In the next lesson, we’ll learn about geometric progression.