Question

There are 'n' rows in a book-shelf. 1st row has 1 book, 2nd row has 3 books, 3rd row has 6 books, 4th row has 10 books and so on. If the total number of books in the shelf is 5456, find the value of 'n'.

• A. 31
• B. 28
• C. 42
• D. 19

Answer 1

The correct option is A 31

We need to find the value of ‘n’ in 1+3+6+10+....... upto n terms = 5456.
This question is based on $\sum \sum n$ concept.
So, $\sum \sum n=\sum \frac{n(n+1)}{2}$
$=\sum \left(\frac{n^2}{2}\right)+\sum \left(\frac{n}{2}\right)$
$=\left\{\frac{n(n+1)(2n+1)}{12}\right\}+\left\{\frac{n(n+1)}{4}\right\}$
$=\frac{n(n+1)(n+2)}{6}$
$AccordingtoQuestion,\frac{n(n+1)(n+2)}{6}=5456$
Putting answer options, we get 31 as the correct answer.