Answer:
483
Step-by-step explanation:
So we have the sequence:
15, 21, 27, 33...
And we want to find the 79th term.
To do so, we can write an explicit formula.
The standard form for an explicit formula for an arithmetic sequence is:
[tex]x_n=a+d(n-1)[/tex]
Where a is the initial term, d is the common difference, and n is the nth term.
From the sequence, we can see that the initial term a is 15.
We can also see that the common difference is +6. This is because each subsequent term is 6 more than the previous one. 15 plus 6 is 21, 21 plus 6 is 27, and so on.
So, substituting 15 for a and 6 for d yields:
[tex]x_n=15+6(n-1)[/tex]
To find the 79th term, substitute 79 for n. So:
[tex]x_{79}=15+6(79-1)[/tex]
Subtract:
[tex]x_{79}=15+6(78)[/tex]
Multiply:
[tex]x_{79}=15+468[/tex]
Add:
[tex]x_{79}=483[/tex]
So, the 79th term is 483.
And we're done!
