Define the derived from the concept of summation notation.

What is the formula for the sum of an arithmetic series.

How to get the Substituting the values.

NCERT Solutions for class 10 Maths chapter 5

Arithmetic Progressions Solutions for Class 10th Maths.

# Find the sums given below: –5 + (–8) + (–11) + . . . + (–230)

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Here, a = – 5 and d = – 8 – (-5) = -3.

Let, the nth term of the A.P. is – 230.

Therefore, a_n = -230

⇒ a + (n -1)d = – 230

⇒ – 5 + (n – 1)(-3) = – 230

⇒ (n – 1)(-3) = -225

⇒ n – 1 = 75 ⇒ n = 76

The sum of n terms of an AP is given by

S_n = n/2[a +l]

⇒ S₇₆ = 76/2[- 5 – 230]

⇒ S₇₆ = 76/2[- 235]

= – 38 × 235 = – 8930

It is an A.P.,

in which, a=−5,d=−8−(−5)=−3,l=−230

First calculate the number in series…..

l=a+(n−1)d

−230=−5+(n−1)−3

−225=−3n+3

3n=228

n=76.

Now,

Sum of the series =

2

n

(a+l)

76/2(−5−230)

38×−235=−8930.

So, the sum of your series would be −8930.