Question

What is the nth term rule of the linear sequence below?
5, 8, 11, 14, 17,...

Answer 1

In a linear series there must be a certain difference between the terms.

• 
  `a_(2)=a_(1)+k`
• 
  `a_(3)=a_(2)+k`
• 
  `a_(n)=a_(n-1)+k`

When you subtract or proportion any term from the term immediately preceding it, the constant you get will be the common difference of the linear series. In the series given in the question, the common difference is
`3.`

• 
  `8-5=3`
• 
  `11-8=3`

Therefore, the general formula of the series must contain the expression
`3n.` Since the first term is
`5`, we will add
`+2`.

Answer:
`a_(n)=3n+2`