Question

21 + 23 + 25 + ⋯ + 43
Find the sum of the arithmetic series

Answer 1

the answer is 384

Explanation:

a1 = 21, a2 = 23, a3 = 25

an = 43

d = a2 - a1 = 23 - 21 = 2

d = a3 - a2 = 25 - 23 = 2

Here, common difference is same everywhere

So,

`a_(n) = a + (n - 1) * d`

`43 = 21 + (n - 1) * 2`

`43 - 21= 2n - 2`

`2n - 2 = 22`

`2n = 24`

`n = 12`

Now,

`s _(n) = (n)/(2) (a + a_(n)) \\`

`s _(12) = (12)/(2) (21+ 43) \\`

`s _(12) = 6 (64) \\`

`s _(12) = 384 \\`