Q. 25.0( 1 Vote )

Find the sum of the series –5+(–8)+(–11)+........+ (–230) ?

Answer :

–5 + (–8) + (–11) + … + (–230)


Let us find the difference of consecutive terms,


a2 – a1 = –8 – (–5) = –3


a3 – a2 = –11 – (–8) = –3


As consecutive differences of terms are same, therefore above series is an AP with


First term, a = –5


Common difference, d = –3


Last term, an = –230


Let the number of terms be ‘n’.


We know, nth term of an AP is


an = a + (n – 1)d


Putting values, we get


–230 = –5 + (n – 1)(–3)


–225 = (n – 1)(–3)


n – 1 = 75


n = 76


We know, the sum of ‘n’ terms of an AP is



Where an is nth term.


Putting values, we get



S76 = 38 × (–235)


S76 = –8930


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