Q21. - Algebra 2

Question

Find the next four terms of each arithmetic sequence.

 6.7, 6.3, 5.9, …

Step-by-Step Solution

Answer

The next four terms of the arithmetic sequence are 5.5, 5.1, 4.7, 4.3.

Step 1. Given Information.

The given arithmetic sequence is 6.7, 6.3, 5.9, …

Step 2. Calculation .

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

 

Here the difference between the first two terms is  $6.3-6.7=-0.4$

The difference between the next two terms is  $5.9-6.3=-0.4$

So, the common difference is -0.4.

 

The next term in the arithmetic sequence is  $5.9-0.4=5.5$

The next term in the arithmetic sequence is  $5.5-0.4=5.1$

The next term in the arithmetic sequence is  $5.1-0.4=4.7$

The next term in the arithmetic sequence is  $4.7-0.4=4.3$

Step 3. Conclusion .

Hence, the next four terms of the arithmetic sequence are 5.5, 5.1, 4.7, 4.3.