Library / /125 of 183

, 2026

Algebra Difficulty 1.8 Junior Find the answer Canada

Beverly creates a sequence of integers. She begins by setting
$\text{sum}=0$ and $\text{a}=1$ . She then writes
down the value of $\text{sum}$ as the first term of the sequence.
Beverly continues the sequence by applying the following steps:

Step 1: She sets $\text{sum}=\text{sum}+\text{a}$ .
Step 2: She writes down the value of $\text{sum}$ as the next
term of the sequence.
Step 3: If $\text{a}=9$ , she stops; otherwise she sets $\text{a}=\text{a}+2$ and returns to Step 1.

What is the last term in Beverly's sequence?

Pick one

Solution

Beverly writes down the value of $\text{sum}$ , which is $0$ , as the first term of the
sequence.

She then sets $\text{sum} = \text{sum} + \text{a} = 0 + 1 = 1$ .

Beverly then writes down the value of $\text{sum}$ , which is $1$ , as the second term of the
sequence.

Since $\text{a}\neq 9$ , she
sets $\text{a} = \text{a} + 2 = 1 + 2 = 3$ and returns to Step 1.

In the table below, we keep track of the values of $\text{sum}$ and $\text{a}$ , as well as the terms of the sequence as Beverly progresses through the steps.

Values of $\text{sum}$
$0$
$0+1=1$
$1+3=4$
$4+5=9$
$9+7=16$
$16+9=25$

Sequence terms
$0$
$1$
$4$
$9$
$16$
$25$

Values of $\text{a}$
$1$
$1+2=3$
$3+2=5$
$5+2=7$
$7+2=9$
stop since $\text{a}=9$

Therefore, the last term in Beverly's sequence is $25$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.