Answer:
We conclude that the rule will be:
aₙ = 31/12 + 1/6n
Step-by-step explanation:
Answer:
we conclude that the rule will be:
[tex]a_n=\frac{31}{12}+\frac{1}{6}n[/tex]
Step-by-step explanation:
Given
The nth term of Arithmetic Sequence
We know the arithmetic sequence with the common difference is defined as
where a₁ is the first term and d is a common difference.
To Determine:
The Rule of the nth term of Arithmetic Sequence
Steps to solve the problem
The 6th term of the Arithmetic sequence be defined as
a₆ = a₁ + (6-1) d
substituting a₆ = 43/12 and a₁ = 11/4 to determine d
43/12 = 11/4 + 5d
switch sides
11/4 + 5d = 43/12
subtract 11/4 from both sides
11/4 + 5d - 11/4 = 43/12 - 11/4
5d = 5/6
Divide both sides by 5
5d/5 = [5/6] / [5]
d = 1/6
as
a₁ = 11/4
d = 1/6
Therefore, the nth term of the Arithmetic sequence will be:
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting d = 1/6 and a₁ = 11/4
aₙ = 11/4 + (n-1) × 1/6
= 11/4 + 1/6n - 1/6
= 31/12 + 1/6n
Therefore, we conclude that the rule will be:
aₙ = 31/12 + 1/6n
