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The sum of the arithmetic (-5) + (-8) + (-11) +.........+ (-230) series is [[1]].

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answer is -8930.

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Detailed Solution

The sum of th arithmetic series (-5) + (-8) + (-11) +.........+ (-230) is -8930.
Given arithmetic series is,
(-5) + (-8) + (-11) +.........+ (-230).
Here,

a = − 5, d = − 8 − − 5 = − 3, a n d a n = − 230

We know that,

a n = a + n − 1 d

Substitute the known values in the formula,

− 5 + (n − 1) × − 3 = − 230 − 5 − 3 n + 3 = − 230 − 2 − 3 n = − 230 3 n = 228 n = 76

There are 76 terms in an AP.
Since,

S n = n 2 [a + l]

where l is the last term

= a n = − 230

.
Substitute the known values in the above formula,

S 76 = 762 [− 5 + (− 230)]

= 28 (− 235) = − 8930

The sum of the arithmetic series is -8930.

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