A club consists of members whose ages are in A.P., the common difference being $$3$$ months. If the youngest member of the club is just $$7$$ years old and the sum of the ages of all the members is $$250$$ years, then the number of members in the club are

Question

A club consists of members whose ages are in A.P., the  common difference being $$3$$ months. If the youngest  member of the club is just $$7$$ years old and the sum  of the ages of all the members is $$250$$ years, then the  number of members in the club are

Infinity Learn · Accepted Answer

$$Sn=n2$$[$$2a+(n$$−$$1)d$$]Here a $$=$$ $$1st$$ term $$=$$ $$7$$ years, d $$=$$ $$3$$ months $$=$$ $$14$$ year,$$Sn=250$$∴ $$250=n22$$×$$7+(n$$−$$1)$$×$$14$$⇒ $$250=n2n+554$$⇒ $$2000=n2+55n$$⇒ $$n2+55n$$−$$2000=0$$⇒ $$(n$$−$$25)(n+80)=0$$⇒$$n=25$$.∴ Number of members in the club $$=$$ $$25$$.

A club consists of members whose ages are in A.P., the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 years, then the number of members in the club are

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