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Find the Sum of the Following Arithmetic Series: (-5)+(-8)+(-11)+...+(-230) - Mathematics

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Question

Find the sum of the following arithmetic series:

(-5)+(-8)+(-11)+...+(-230)

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Solution

The given arithmetic series is  (-5)+(-8)+(-11)+...+(-230)

Here , a = -5 , d = -8 -(-5) = -8 + 5= -3 and l = 230

Let the given series contain n terms. Then,

an = -230 

 ⇒ -5 + (n-1) × (-3) = -230               [ a = a + (n-1) d]

⇒ - 3n - 2 = -230 

⇒ -3n = -230 + 2 = -228 

⇒ n = 76 

`∴ "Required sum" = 76/2 xx [ ( -5) + (-230) ]            [ s_n = n/2 (a+l)]`

`= 76/2 xx (-235) `

= - 8930

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Chapter 11: Arithmetic Progression - Exercises 4

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R.S. Aggarwal Mathematics [English] Class 10
Chapter 11 Arithmetic Progression
Exercises 4 | Q 2.3

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