Some chocolates are distributed between 25 children in such a way that first child gets 5, 2nd gets 7 chocolates - Maths - Sequences and Series

Question

Some chocolates are distributed between 25 children in such a way
that first child gets 5, 2nd gets 7 chocolates and in general nth
child gets n chocolates more than the n-1 th child The total number
of chocolates distributed is? Answer 3025

Ishwarmani · Accepted Answer

Dear
Student,
Please
find below the solution to the asked query:

Sum=5+7+10+14+19+
   25 terms         =4+1+4+1+2+4+1+2+3+4+1+2+3+4+
4+1+2+3+4+ +25Here, an=4+1+2+3+
+n=4+nn+12=n2+n+82∴ S25=∑n=125an⇒S25=∑n=125n2+n+82           =12∑n=125n2+n+8           =12∑n=125n2+∑n=125n+∑n=1258           =122525+150+16+2525+12+8×25           =1225×26×516+25×262+8×25           =1225×13×17+25×13+8×25           =25213×17+13+8           =25213×18+8           =25×2422            =3025

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Some chocolates are distributed between 25 children in such a way that first child gets 5, 2nd gets 7 chocolates and in general nth child gets n chocolates more than the n-1 th child. The total number of chocolates distributed is? Answer 3025