Question

A picnic group consists of students whose ages are in A P, the common difference being 3 months. If the youngest student is just 7 years old and the sum of the ages of all the students is 250 years, find the number of students in the group
pls reply as fast as possible

Answer 1

a = 7
d = 3months, 3/12 = 1/4
Sn = 250

Sn = n/2(2a + (n-1)d)
250 = n/2(2(7) + (n-1)1/4)
250(2) = n(14 + (1/4n - 1/4)

Multiply, the whole equation by 4 to cancel the denominators.

=>n (56 + n - 1) 500(4)
56n + n^2 - n) 2000 n^2 + 55n - 2000 = 0 Now, Factorize n^2 + 80n - 25n - 2000 = 0 n(n + 80) 25(n + 80) = 0 (n - 25) (n + 80) = 0 Therefore, n = +25 or -80 Number of students cannot be negative so we reject the negative number and take the positive number which is n = 25 So, the number of students is 25.. Hope it helps!! Mark it as the brainliest answer!

Answer 2

Let the number of the students involved in the picnic be n.

Given conditions ⇒

First term(a) = 7 years.
Sum of the ages(Sn)  = 250 years.
Common difference(d) = 3 months. 
= 3/12 years.
= 1/4 years.

Now,
Using the Formula,

Sn = n/2[2a + (n - 1)d]
250 = n/2[2 × 7 + (n - 1)1/4]
250 = n/2[56 + n - 1]/4
n[55 + n]/8 = 250
55n + n² = 2000
⇒ n² + 55n - 2000 = 0
Splitting the Middle term,
n² + 80n - 25n - 2000 = 0
n(n + 80) - 25(n + 80) = 0
(n - 25)(n + 80) = 0
n = 25 and n = -80


Since, -80 cannot be possible, Therefore rejecting it.

Hence, the number of the students in the group is 25.


Hope it helps.