Question

First term: 2 3/4 sixth term: 3 7/12

Answer 1

We conclude that the rule will be:

aₙ = 31/12 + 1/6n

Explanation:

Answer:

we conclude that the rule will be:

`a_n=(31)/(12)+(1)/(6)n`

Explanation:

Given

• 
  `a_6=3(7)/(12)=(43)/(12)`

• 
  `a_1=2(3)/(4)=(11)/(4)`

The nth term of Arithmetic Sequence

We know the arithmetic sequence with the common difference is defined as

• 
  `a_n=a_1+\left(n-1\right)d`

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:

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

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