We have been asked to calculate the sum given below. (i) 34+32+30+….+10. (ii) (−5)+(−8)+(−11)+…..+(−230)
ML Aggarwal Avichal Publication
Arithmetic Progression chapter 9 question no 2
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(i) 34,32,30....................10
Here a=34,l=10
d=32−34=−2
an=a+(n−1)d
10=34+(n−1)(−2)⇒10−34=(−2)(n−1)⇒n−1=12⇒n=13
and last term l=10
We know that Sn=2n(a+l)
Sn=213(34+10)
=213×44
=286
(ii) −5+(−8)+(−11)+...........+(−230)
Here a=−5,l=−230
d=(−8−(−5))=−3
an=a+(n−1)d
230=−5+(n−1)(−3)⇒−230+5=(−3)(n−1)⇒n−1=75⇒n=76
and last term l=−230
We know that Sn=2n(a+l)
Sn=276(−5+(−230)
=−8930