A basic and conceptual question from arithmetic progression chapter in which we are to find the sum of the given arithmetic series
7 + 10 1/2 + 14 +….+ 84.
RS Aggarwal, Class 10, chapter 5C, question no 2(i).
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In given series of AP first term a=7, common difference d= 1021​−7=221​−7=27​ and last term l=84
Since, l=a+(n−1)d
⇒84=7+(n−1)27​
⇒84−7=(n−1)27​
⇒77=(n−1)27​
⇒77×72​=n−1
⇒22=n−1
⇒n=23
Since, Sn​=n​/2(a+l)
⇒Sn​=23/2​(7+84)
⇒Sn​=91×23/2​
⇒Sn​=2093/2​
⇒Sn​=1046 1/2​