Question

What is the explicit formula for the arithmetic sequence in the table below? n 1 2 3 4 5 an 9.2 7.4 5.6 3.8 2

Answer 1

Commin difference  d = 7.4 - 9.2 = -1.8  and first term a1 = 1   so the explicit formula is  

an = 9.2 +(n - 1)*-1.8   

an =  9.2 - 1.8(n - 1)

Answer 2

Answer:

$a_{n}=9.2-1.8(n-1)$

Step-by-step explanation:

An explicit formula is useful to find the terms of a sequence while the Recursive Formula is useful to find the Arithmetic Sequence as a function. So let's write the Explicit formula, considering the data and the behavior of this Arithmetic Sequence. The Common difference for this sequence is -1.8. So, we have a decreasing Arithmetic Sequence, as we can see in the graph below.

$n_{1},n_{2},n_{3},n_{4},n_{5}\Rightarrow a_{1},a_{2},a_{3},a_{4},a_{5}\\\left \{ 9.2,7.4,5.6,3.8,2 \right \}\\\: a_{1}=9.2\: \: a_{n-1}+d=a_{n}\Rightarrow 7.4+d=9.2\Rightarrow d=-1.8\\a_{2}=a_{1}+d\:a_{3}=a_{2}+d\: a_{4}=a_{3}+d \:a_{5}=a_{4}+d \\7.4=9.2-1.8\\5.6=7.4-1.8\\3.8=5.6-1.8\\2=3.8-1.8\\\\\Rightarrow a_{n}=9.2-1.8(n-1)$