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Q11.

Expert-verifiedFound in: Page 581

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**68 is the ___?__ th term of the arithmetic sequence -2, 3, 8, ... . **

68 is the** 15th term **of the arithmetic sequence -2, 3, 8, ....

Given arithmetic sequence is -2, 3, 8, ...

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

Here the first term is ${a}_{1}=-2$

The difference between the first two terms is $3-(-2)=3+2=5$

The difference between the second two terms is $8-3=5$

The common difference is $d=5$

The given nth term is ${a}_{n}=68$

Plugging the values in the formula:

$\begin{array}{l}{a}_{n}={a}_{1}+(n-1)d\\ 68=-2+(n-1)\left(5\right)\\ 68+2=(n-1)\left(5\right)\\ (n-1)\left(5\right)=70\\ n-1=\frac{70}{5}\\ n-1=14\\ n=14+1\\ n=15\end{array}$

Hence, 68 is the 15^{th} term of the arithmetic sequence -2, 3, 8, ... .

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