Question

Write an explicit formula for a,, the nth
term of the sequence 39, 45, 51, ....

Answer 1

`a_n=33+6n`

Explanation:

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

Given terms:

• 
  `a_1=39`
• 
  `a_2=45`
• 
  `a_3=51`

To find the common difference, subtract a term from the next:

`d=a_3-a_2=51-45=6`

Substitute
`a=39` and
`d=6` into the formula:

`\implies a_n=39+6(n-1)`

`\implies a_n=39+6n-6`

`\implies a_n=33+6n`