# Find the Sum (−5) + (−8)+ (−11) + ... + (−230) . - Mathematics

Sum

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

#### Solution

(−5) + (−8)+ (−11) + ... + (−230) .

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

=-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,

an =  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  Sn = -8930

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 13.3 | Page 51