### Home > PC > Chapter 2 > Lesson 2.1.2 > Problem2-30

2-30.

Brian has the following sums to find:

$\begin{array}{l} 1 + 3 \\ 1 + 3 + 5 \\ 1 + 3 + 5 + 7 \\ \qquad \quad \; . \\ \qquad \quad \; . \\ \qquad \quad \; . \\ 1 + 3 + 5 + 7 + \dots ​+ 101 \end{array}$

Find a shortcut so that he will not have to add the last sum by hand.

$1+3=4$ or $2^2$ (How many terms are in the sum?)

$1+3+5=9$ or $3^2$ (How many terms are in the sum?)

$1+3+5+7=16$ or $4^2$ (How many terms are in the sum?)

(How many terms are in the final sum?)