Question

It's Shreya's Birthday. There are 20 students in her class, numbered 1 to 20. She gives 8 chocolates to student 1, 10 more than 8 chocolates to student 2, and progresses in such a way that each succeeding student gets 10 chocolates more than each preceding student. What is the exact number of chocolates Shreya needs to buy such that the chocolates are exactly sufficient?

• A. 4080
• B. 2060
• C. 678
• D. 409

Answer 1

The correct option is B

2060

8 chocolates to Student 1.
8 + 10 Chocolates to Student 2.
8 + 10 + 10 Chocolates to Student 3.
8, 18, 28,..
The sequence of Number of Chocolates distributed to each student forms an A.P with initial term equal to 8 and common difference equal to 10
Given that total number of Students = 20
$\therefore$ Number of terms is also 20
$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$
$S_n=\frac{20}{2}\left(2\right(8)+(20-1\left)10\right)$
$S_n=10(16+19\times 10)$
$S_n=10(16+190)$
$S_n=2060$
The number of chocolates she needs to buy is 2060