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 numbers is 250 years, then the number of members in the club are –

• A. 15
• B. 25
• C. 20
• D. 30

Answer 1

Answer: (B)

25

Answer 2

S_n = $\frac{n}{2}$ [2a + (n – 1)d]

Here a = 1^st term = 7 years, d = 3 months = $\frac{1}{4}$year,

S_n = 250 years.

250 = $\left\lbrack 2 \times 7 + (n - 1) \times \frac{1}{4} \right\rbrack$

̃ 250 =$\left( \frac{n + 55}{4} \right)$

̃ 2000 = n² + 55n ̃ n² + 55n – 2000 = 0

̃ (n – 25) (n + 80) = 0 ̃ n = 25

\ Number of members in the club = 25.