Question

After a drought, the village landlord decided to open the granary for the villagers. The distribution
pattern was that in a family the youngest member got 2 Kg and in order of age the next person got 1.5 Kg more than the member younger to him .

a) If a family received 87.5 kg , how many members were there ?

Answer 1

n/2 { 2x2 + (n-1)x1.5 } = 87.5

n/2 { 4 + 1.5n - 1.5 } = 87.5

n/2 { 2.5 + 1.5n} =87.5

2.5n /2 + 1.5n²/2 = 87.5

2.5n+1.5n² / 2 = 87.5

1.5n² + 2.5n = 175

solving the eq we get n = 10

Answer 2

This is the problem of AP because the difference between each member is same (1.5) .
let n is the number of terms of an AP and Sn is the sum, then
Sn=n/2[ 2a+(n−1)d ]

Where d is common difference and a is the first term.
So , 87.5= n/2 [ 2×2+(n-1)1.5]

87.5×2 = n/2 [ 4+1.5n-1.5]

175 = 2.5n+1.5n^2

1.5n^2 +2.5n- 175 =0

so, n = 10
so, there are 10 members in the family.
thank Getitfast for finding the mistake.