Question

Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms

Answer 1

In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,

`S_n = n/2 [2a + (n -1)d]`

Where; a = first term for the given A.P.

d = common difference of the given A.P.

n = number of terms

−26, −24, −22, …. to 36 terms

Common difference of the A.P. (d) = `a_2 - a_1`

= (-24) - (-26)

= - 24 + 26

= 2

Number of terms (n) = 36

The first term for the given A.P. (a) = −26

So, using the formula we get,

`S_36 = 36/2 [2(-26) + (36 - 1)(2)]`

= (18)[-52 + (35) (2)]

= (18)[-52 + 70]

= (18)[18]

= 324

Therefore the sum of first 36 terms for the given A.P is 324