Question

Which function represents the sequence: 4, 7, 10, 13, 16,...

Answer 1

`\large\boxed{a(n)=3n+1}`

Explanation:

It's an arithmetic sequence:

`a(1)=4\\\\a(2)=a(1)+3=4+3=7\\\\a(3)=a(2)+3=7+3=10\\\\a(4)=a(3)+3=10+3=13\\\\a(5)=a(4)+3=13+3=16\\\vdots`

An explicit formula of an arithmetic sequence:

`a(n)=a(1)+(n-1)d`

d - common difference

We have

`a(1)=4,\ d=3`

Substitute:

`a(n)=4+(n-1)(3)` use the distributive property

`a(n)=4+3n-3`

`a(n)=3n+1`

Answer 2

3n + 1

Explanation:

Note the sequence has a common difference between consecutive terms, that is

7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3

This indicates that the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 4 and d = 3, thus

`a_(n)` = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1