Q. 2 C3.8( 15 Votes )

Find the sum of each of the following arithmetic series:

(-5) + (-8) + (-11) + … + (-230)

Answer :

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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