Question

a picnic group for Shimla consists students of whose ages are in arithmetic progression the common difference is 3 months the youngest student Neeraj is just 12 years old the sum of the ages is 375 years find the number of students in the group

Answer 1

it is given that,

d=3

a=12

an=375

we know that,

an=a+(n-1)d

375=12+(n-1)3

375=12+3n-3

375=9+3n

375-9=3n

366=3n

366÷3=n

122=n

hence total number of student in the group are 122

Answer 2

Answer:

There are 25 students in the group.

Step-by-step explanation:

a=12           d=3 months=1/4 year

Sn=375

n/2(2a+(n-1)d)=375

n/2(2*12+(n-1)1/4)=375

n/2(24+n/4-1/4)=375

n/2(96/4-1/4+n/4)=375

n/2(95/4+n/4)=375

95n/8+n²/8=375

(95n+n²)/8=375

95n+n²=3000

n²+95n-3000=0

By splitting the middle term,

n²+120n-25n-3000=0

n(n+120)-25(n+120)=0

(n+120)(n-25)=0

n+120=0                 n-25=0

n=-120                     n=25

As number of students cannot be negative we don't consider n=-120.

∴Total number of students are 25.