Question

The natural numbers are divided into rows as follows
$\begin{array}{ccccc}& & 1& & \\ & 2& 3& 4& \\ 5& 6& 7& 8& 9\end{array}$
The sum of the numbers in the ${10}^{t}h$ row is

• A. 1720
• B. 1721
• C. 1723
• D. 1729

Answer 1

The correct option is D 1729

$r^{th}$ row contains 2r – 1 numbers and ends with $r^2$ the ${10}^{th}$ row contains 19 numbers, ends with ${10}^2=100$ and begins with $9^2+1=82$
The sum of the numbers in the ${10}^{th}raw=\frac{19}{2}(82+100)=19\times 91=1729$