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

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Solution

The correct option is B 25
$H e r e, a = 1^{s t} t e r m = 7 y r, d = 3 m o n t h s = \frac{1}{4} y r S_{n} = 250 y r ∴ 250 = \frac{n}{2} [2 \times 7 + (n - 1) \times \frac{1}{4}] \Rightarrow 250 = \frac{n}{2} (\frac{n + 55}{4}) \Rightarrow 200 = n^{2} + 55 n \Rightarrow n^{2} + 55 n - 2000 = 0 = (n - 25) (n + 80) = 0 \Rightarrow n = 25$
$∴$ Number of members in the club =25

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

The correct option is B 25Here,a=1st term=7yr,d=3 months=14yrSn=250yr∴250=n2[2×7+(n−1)×14]⇒250=n2(n+554)⇒200=n2+55n⇒n2+55n−2000=0=(n−25)(n+80)=0⇒n=25 ∴ Number of members in the club =25

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