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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

Respuesta :

calculista

Answer:

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

Step-by-step explanation:

we know that

The formula of an arithmetic sequence is

[tex]a_n=a_1+(n-1)d[/tex]

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

[tex]a_1=-4\\a_4=5\\a_1_0=23[/tex]

so

[tex]a_4=a_1+(4-1)d\\5=-4+(4-1)d\\5=-4+3d\\3d=5+4\\d=3[/tex]

so

[tex]a_n=a_1+3(n-1)[/tex]

[tex]a_n=-4+3n-3[/tex]

[tex]a_n=3n-7[/tex]

therefore

[tex]f(n)=3n-7[/tex]

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