Answer:
[tex]\displaystyle a_n=100+10(n-1)[/tex]
[tex]\displaystyle a_{10}=190[/tex]
Step-by-step explanation:
We have the arithmetic sequence:
100, 110, 120, 130...
And we want to determine the equation for the nth term of the sequence.
The standard form for the nth term of an arithmetic sequence is given by the formula:
[tex]\displaystyle a_n=a+d(n-1)[/tex]
Where [tex]a_n[/tex] is the nth term, [tex]a[/tex] is the first term, and [tex]d[/tex] is our common difference.
From the sequence, we can see that the first term [tex]a[/tex] is 100.
Also, each term is +10 the previous term. Hence, our common difference [tex]\displaystyle d[/tex] is +10.
Therefore, our equation is:
[tex]\displaystyle a_n=100+10(n-1)[/tex]
To find the 10th term, we can substitute 10 for n and evaluate. Hence:
[tex]\displaystyle a_{10}=100+10(10-1)[/tex]
Evaluate:
[tex]\displaystyle a_{10}=100+10(9)=100+90=190[/tex]
Therefore, the 10th term is 190.
