Q52. - Algebra 2

Question

Find the arithmetic means in each sequence.

 55,  ? ,  ? ,  ? , 115 

Step-by-Step Solution

Answer

The arithmetic means in the sequence are 70, 85, 100.

Step 1. Given Information.

Given there are three arithmetic means between 55 and 115.

Step 2. Calculation .

The n^th term of an arithmetic sequence is given by$a_n=a_1+(n-1)d$  .

 

Since there are three arithmetic means between 55 and 115,

The first term is  $a_1=55$

And the fifth term is  $a_5=115$

 Plugging the values in the formula:  

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_5=a_1+(5-1)d\\ 115=55+4d\\ 4d=115-55\\ 4d=60\\ d=15\end{array}$

Hence the common difference is 15.

Since the first term in the arithmetic sequence is 55:

The next term in the arithmetic sequence is  $55+15=70$

The next term in the arithmetic sequence is  $70+15=85$

The next term in the arithmetic sequence is  $85+15=100$

And the fifth term in the arithmetic sequence is 115.

            

Step 3. Conclusion .

Hence, the arithmetic means in the sequence are 70, 85, 100.