Q. 2 C3.8( 15 Votes )

# Find the sum of each of the following arithmetic series:(-5) + (-8) + (-11) + … + (-230)

Here, First term = - 5

Common difference = d = - 8 - (-5) = - 3

Last term = l = - 230

Now, - 230 = a + (n - 1)d

- 230 = - 5 + (n - 1)(-3)

- 230 + 5 = (n - 1)(-3)

- 225 = - 3n + 3

- 225 - 3 = - 3n

- 228 = - 3n

n = 76

there are 76 terms in this Arithmetic series.

Now, Sum of these 76 terms is given by

S76 = [2(-5) + (76 - 1)(-3)]

= 38 × [ - 10 + (75)(-3) ]

= 38 × [ - 10 - 225]

= 38 × (-235)

= - 8930

Thus, sum of 23 terms of this AP - 8930.

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