In a class of students, the first student has 2 toffees, second has 4 toffees, third has 6 toffees and so on. If the number of students in the class is 25, then the total number of toffees are divisible by ________.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2. i.e. 5 and 13.
Given:
First student has 2 toffees,
Second student has 4 toffees, and
Third student has 6 toffees and so on.
Concept Used:
Sum of n terms of AP = ½ (L + A) × n ....(i)
nth term of AP = A + (n - 1)D ...(ii)
Where, L = last term, A = first term, D = common difference, n = number of terms
Explanation:
The number of toffees are in AP, where first term is 2.
Common difference = (4 - 2) = 2
The number of toffees with last (25th ) student = 2 + (25 - 1) × 2 = 50 toffees {using equation (ii)}
Now, sum of toffees = ½ (2 + 50) × 25 {using equation (i)}
⇒ sum of toffees = 26 × 25 = 13 × 2 × 52
Hence the total number of toffees are divisible by 5 and 13.