Question

Please help ASAP!

The first term in an arithmetic sequence is -4. The fourth term in the sequence is 5. The tenth term in the sequence is 23. Which function can be used to find the nth term of the arithmetic sequence?
A: f(n) = -4 + 1/3(n -1)
B: f(n) = n - 4
C: f(n) = 3n - 7
D: f(n) = 3n

Answer 1

Option C: f(n) = 3n - 7

Explanation:

we know that

The formula of an arithmetic sequence is

`a_n=a_1+(n-1)d`

where

a_n is the nth term in the sequence

a_1 is the first term in the sequence

d is the common difference

In this problem we have

`a_1=-4\\a_4=5\\a_1_0=23`

so

`a_4=a_1+(4-1)d\\5=-4+(4-1)d\\5=-4+3d\\3d=5+4\\d=3`

so

`a_n=a_1+3(n-1)`

`a_n=-4+3n-3`

`a_n=3n-7`

therefore

`f(n)=3n-7`