Question

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

Short answer

68 is the15th termof the arithmetic sequence -2, 3, 8, ....

Step-by-step solution

Step 1. Given Information.

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

Step 2. Calculation.

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:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ 68=-2+(n-1)\left(5\right)\\ 68+2=(n-1)\left(5\right)\\ (n-1)\left(5\right)=70\\ n-1=\frac{70}{5}\\ n-1=14\\ n=14+1\\ n=15\end{array}$

Step 3. Conclusion.

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