Q36. - Algebra 2

Question

Find the indicated term of each arithmetic sequence.

$a_1=\frac{5}{2},d=-\frac{3}{2},n=11$

Step-by-Step Solution

Answer

The indicated term of the arithmetic sequence is $-\frac{25}{2}$ .

Step 1. Given Information.

Given indicated term of arithmetic sequence is  $a_1=\frac{5}{2},d=-\frac{3}{2},n=11$

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  $a_1=\frac{5}{2}$

The common difference is  $d=-\frac{3}{2}$

And the required term is  $n=11$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{11}=\frac{5}{2}+(11-1)(-\frac{3}{2})\\ a_{11}=\frac{5}{2}+\left(10\right)(-\frac{3}{2})\\ a_{11}=\frac{5}{2}-\frac{30}{2}\\ a_{11}=-\frac{25}{2}\end{array}$

Step 3. Conclusion .

Hence, the indicated term of the arithmetic sequence is $-\frac{25}{2}$ .