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Algebra Difficulty 1.3 Junior Find the answer Canada

An expression that produces the values in the second row of the table shown, given the values of $n$ in the first row, is

$n$
1
2
3
4
5

value
1
3
5
7
9

Pick one

Solution

When $n=4$ , we are looking for an expression that produces a value of 7.
The results of substituting $n=4$ into each expression and evaluating are shown below.

Expression
Value

(A) $3n-2$
$3(4)-2=12-2=10$

(B) $2(n-1)$
$2(4-1)=2(3)=6$

(D) $2n$
$2(4)=8$

(E) $2n-1$
$2(4)-1=8-1=7$

Since $2n-1$ is the only expression which gives a value of 7 when $n=4$ , it is the only possible answer. We check that the expression $2n-1$ does give the remaining values, $1,3,5,9$ , when $n=1,2,3,5$ , respectively.
(Alternately, we may have began by substituting $n=1$ and noticing that this eliminates answers (B), (C) and (D). Substituting $n=2$ eliminates (A). Substituting $n=3$ , $n=4$ and $n=5$ confirms the answer (E).)

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