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Q16.

Expert-verifiedFound in: Page 523

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****.**

$16,4,-8,-20,\mathrm{...}$

The next three terms of the given arithmetic sequence are $\mathbf{-}\mathbf{32}\mathbf{,}\mathbf{-}\mathbf{44}$ **and $\mathbf{-}\mathbf{56}$.**

The given arithmetic sequence is: $16,4,-8,-20$.

From the given arithmetic sequence, it can be noticed that the first, second, third, and fourth terms of the arithmetic sequence are $16,4,-8$ and $-20$ respectively.

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:

$d=4-16\phantom{\rule{0ex}{0ex}}=-12$

Therefore, the first term and the common difference of the given arithmetic sequence are 16 and $-12$ respectively.

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 a 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 ${a}_{1}=16$ and $d=-12$ are:

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

$=16+\left(4\right)\left(-12\right)\phantom{\rule{0ex}{0ex}}=16-48\phantom{\rule{0ex}{0ex}}=-32$

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

$=16+\left(5\right)\left(-12\right)\phantom{\rule{0ex}{0ex}}=16-60\phantom{\rule{0ex}{0ex}}=-44$

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

$=16+\left(6\right)\left(-12\right)\phantom{\rule{0ex}{0ex}}=16-72\phantom{\rule{0ex}{0ex}}=-56$

Therefore, the next three terms of the given arithmetic sequence are $-32,-44$ and $-56$.

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