Question

Describe the relationship between the terms in each arithmetic sequence. Then write the next three terms in the sequence.

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

0.4, 0.8, 1.2, 1.6, ...

An Arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

Computing the differences of all the adjacent terms

$0.8-0.4=0.4,\:\quad \:1.2-0.8=0.4,\:\quad \:1.6-1.2=0.4$

The difference between all the adjacent terms is the same and equal to

$d=0.4$

As the first element of the sequence is

$a_1=0.4$

Thus, the relationship between the terms in each arithmetic sequence can be determined by using the formula

$a_n=a_1+\left(n-1\right)d$

substituting $a_1=0.4$, and $d=0.4$

$a_n=0.4\left(n-1\right)+0.4$

$a_n=0.4n$

Therefore, the relationship between the terms in each arithmetic sequence is:

• $a_n=0.4n$

Finding the next three terms:

Given the sequence

$a_n=0.4n$

putting n = 5 to determine the 5th term

$a_5=0.4\left(5\right)$

$a_5=2$

putting n = 6 to determine the 6th term

$a_6=0.4\left(6\right)$

$a_6=2.4$

putting n = 7 to determine the 7th term

$a_7=0.4\left(7\right)$

$a_7=2.8$

Therefore, the next three terms are:

• $a_5=2$

• $a_6=2.4$

• $a_7=2.8$