Question

Find the sum  (−5) + (−8)+ (−11) + ... + (−230) .

Answer 1

(−5) + (−8)+ (−11) + ... + (−230) .

Common difference of the A.P. (d) = a₂ - a₁ 

=-8-(-5)

=-8+5

=-3

So here,

First term (a) = −5

Last term (l) = −230

Common difference (d) = −3

So, here the first step is to find the total number of terms. Let us take the number of terms as n.

Now, as we know,

a_n =  a + (n-1) d

So, for the last term,

   - 230 = -5 + ( n-1) (-3) 

   - 230 = -5-3n + 3

-23 +2 = -3n

`(-228)/(-3) = n`

           n = 76

Now, using the formula for the sum of n terms, we get

`S_n = 76/2 [2(-5) + (76-1) (-3)]`

      = 38 [-10+(75)(-3)]

      =38 (-10-225)

      = 38(-235)

      = -8930

Therefore, the sum of the A.P is  S_n = -8930