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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 [ an = 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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