Question

Find the sum of the following arithmetic progressions:

1, 3, 5, 7, ... to 12 terms

Answer 1

1, 3, 5, 7, ... to 12 terms

Common difference of the A.P. (d)

`= a_2 - a_1`

= 3 - 1

= 2

Number of terms (n) = 12

First term for the given A.P (a) = 1

So using the formula we get

`S_n = 12/2 [2(1) = (12 - 1)(2)]`

 = (6)[2 + (11)(2)] 

= (6)[24]

= 144

Therefore, the sum of first 12 terms for the given A.P. is 144