Question

Find a formula for the nth term in this

arithmetic sequence:
a₁ = -7, a2 = -1, a3 = 5, a4 = 11, ...
an = [? ]n + [ ]

Answer 1

`a_n=6n-13`

Explanation:

Arithmetic sequence

General form of an arithmetic sequence:
`a_n=a+(n-1)d`

where:

• 
  `a_n` is the nth term
• a is the first term
• d is the common difference between terms

Given:

• 
  `a_1=-7`
• 
  `a_2=-1`
• 
  `a_3=5`
• 
  `a_4=11`

To find the common difference, subtract consecutive terms:

`\implies d=a_4-a_3=11-5=6`

Therefore, the formula for the nth term is:

`\implies a_n=-7+(n-1)6`

`\implies a_n=-7+6n-6`

`\implies a_n=6n-13`