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.