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Q43.

Expert-verifiedFound in: Page 582

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Complete the statement for each arithmetic sequence.**

** ****170 is the ___?__ term of -4, 2, 8, ... . **

170 is the** 30th **term of the arithmetic sequence -4, 2, 8, **… .**

Given arithmetic sequence is -4, 2, 8, ...

The *n*^{th} term of an arithmetic sequence is given by${a}_{n}={a}_{1}+(n-1)d$ .

Here the first term is ${a}_{1}=-4$

The difference between the first two terms is $2-(-4)=2+4=6$

The difference between the second two terms is $8-2=6$

The common difference is $d=6$

The given nth term is ${a}_{n}=170$

Plugging the values in the formula:

$\begin{array}{l}{a}_{n}={a}_{1}+(n-1)d\\ 170=-4+(n-1)\left(6\right)\\ 170+4=(n-1)\left(6\right)\\ (n-1)\left(6\right)=174\\ n-1=\frac{174}{6}\\ n-1=29\\ n=29+1\\ n=30\end{array}$

Hence, 170 is the 30th term of the arithmetic sequence -4, 2, 8, … .

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