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Q17.

Expert-verified
Found in: Page 523

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

# Find the next three terms of each arithmetic sequence.$2,10,18,26,...$

The next three terms of the given arithmetic sequence are 34, 42 and 50.

See the step by step solution

## Step 1. Find the first term of the given arithmetic sequence.

The given arithmetic sequence is: $2,10,18,26,...$

From the given arithmetic sequence, it can be noticed that the first, second, third and fourth terms of the arithmetic sequence are 2, 10, 18 and 26 respectively.

## Step2. Finding the common difference

The common difference of the arithmetic sequence is the difference between the succeeding term and its preceding term.

Therefore, the common difference $\left(d\right)$ of the given arithmetic sequence is:

$d=10-2\phantom{\rule{0ex}{0ex}}=8$

Therefore, the first term and the common difference of the given arithmetic sequence are 2 and 8 respectively.

## Step 3. Find the next three terms of the given arithmetic sequence.

The $n\mathrm{th}$ term $\left({a}_{n}\right)$ of the given arithmetic sequence is given by:

${a}_{n}={a}_{1}+\left(n-1\right)d$, where ${a}_{1}$ is the first term and $d$ is the common difference.

The next three terms of the given arithmetic sequence are fifth, sixth and seventh terms.

Therefore, the next three terms of the given arithmetic sequence having ${a}_{1}=2$ and $d=8$ are:

${a}_{5}={a}_{1}+\left(5-1\right)d$

$=2+\left(4\right)\left(8\right)\phantom{\rule{0ex}{0ex}}=2+32\phantom{\rule{0ex}{0ex}}=34$

${a}_{6}={a}_{1}+\left(6-1\right)d$

$=2+\left(5\right)\left(8\right)\phantom{\rule{0ex}{0ex}}=2+40\phantom{\rule{0ex}{0ex}}=42$

${a}_{7}={a}_{1}+\left(7-1\right)d$

$=2+\left(6\right)\left(8\right)\phantom{\rule{0ex}{0ex}}=2+48\phantom{\rule{0ex}{0ex}}=50$

Therefore, the next three terms of the given arithmetic sequence are 34, 42 and 50.