Question

Formula for sum of n terms in arithmetic progression

Answer 1

The formula for sum of n terms in arithmetic progression,

$S_{n}$ = $\dfrac{n}{2}$ {2a + (n - 1)d}

                                         or

$S_{n}$ = $\dfrac{n}{2}$ {a + l}

Step-by-step explanation:

The formula for sum of n terms in arithmetic progression,

$S_{n}$ = $\dfrac{n}{2}$ {2a + (n - 1)d} .... (1)

Where, a is the first term of an arithmetic progression,

d is the common difference of an arithmetic progression,

d is the $n^{th}$ number of terms of an arithmetic progression,

$S_{n}$  is the sum $n^{th}$  terms of an arithmetic progression

We also know that,

$a_{n}$ = a + ( n - 1 ) d = l ..... (2)

where, $a_{n}$ = l is the $n^{th}$ term of an arithmetic progression

From equations (1) and (2), we get

$S_{n}$ = $\dfrac{n}{2}$ {a + l}

The formula for sum of n terms in arithmetic progression,

$S_{n}$ = $\dfrac{n}{2}$ {2a + (n - 1)d}

or

$S_{n}$ = $\dfrac{n}{2}$ {a + l}