Question

25 points+brainliest!

Answer 1

Answer:

an= 10n+90

a10= 190

Answer 2

Answer:

$\displaystyle a_n=100+10(n-1)$

$\displaystyle a_{10}=190$

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:

$\displaystyle a_n=a+d(n-1)$

Where $a_n$ is the nth term, $a$ is the first term, and $d$ is our common difference.

From the sequence, we can see that the first term $a$ is 100.

Also, each term is +10 the previous term. Hence, our common difference $\displaystyle d$ is +10.

Therefore, our equation is:

$\displaystyle a_n=100+10(n-1)$

To find the 10th term, we can substitute 10 for n and evaluate. Hence:

$\displaystyle a_{10}=100+10(10-1)$

Evaluate:

$\displaystyle a_{10}=100+10(9)=100+90=190$

Therefore, the 10th term is 190.