Question
Download Solution PDFIn 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 .
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In a class of students, the first student has 2 toffees, the second has 4 toffees, the third has 6 toffees, and so on.
Concept used:
1. Number of terms of an AP = (L - A)/D + 1
2. Sum of N terms of an AP = (L + A)/2 × N
3. Nth term = A + (N - 1) × D
(Where L = Last Term, A = First Term and D = Common Difference)
Calculation:
The number of toffees according to the number of students is in an Arithmetic Progression where
2 = First Term
(4 - 2) = (6 - 4) = ... = 2 = Common Difference
So, the number of toffees 25th student will get = 2 + (25 - 1) × 2 = 50
Now, the total number of toffees
⇒ (2 + 50)/2 × 25
⇒ 26 × 25
⇒ 2 × 52 × 13
∴ The total number of toffees is divisible by 5 and 13.
Last updated on Jul 14, 2025
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