Answer:
-496
Step-by-step explanation:
The direct formula for the nth term of an arithmetic sequence is given by the formula:
[tex]x_n=a\cdot d(n-1)[/tex]
Where a is the initial term, d is the common ratio, and n is the nth term.
Let's find a and d.
From the sequence, we can see that the initial term or a is 26.
Also, each subsequent term is 9 less than the previous term. In other words, our common ratio is -9.
Therefore, our direct formula is:
[tex]x_n=26-9(n-1)[/tex]
To find the 59th term, substitute 59 for n:
[tex]x_{59}=26-9(59-1)[/tex]
Subtract:
[tex]x_{59}=26-9(58)[/tex]
Multiply:
[tex]x_{59}=26-522[/tex]
Subtract:
[tex]x_{59}=-496[/tex]
So, the 59th term is -496.
And we're done!
