Answer:
If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is ![\mathbf{d(n)=8+2n\:for\:n>1}](https://tex.z-dn.net/?f=%5Cmathbf%7Bd%28n%29%3D8%2B2n%5C%3Afor%5C%3An%3E1%7D)
Option D is correct option
Step-by-step explanation:
We are given the arithmetic sequence:
10, 12, 14, 16, ...
If n is an integer, which of these functions generate the sequence?
We need to find the nth term for the given sequence
The nth term for arithmetic sequence will be: ![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
where aₙ is nth term, a₁ is first term and d is common difference
Looking at the sequence a₁ = 10 and d = 2
So, nth term will be:
![a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5Ca_n%3D10%2B%28n-1%292%5C%5Ca_n%3D10%2B2n-2%5C%5Ca_n%3D8%2B2n)
So, nth term is: ![a_n=8+2n](https://tex.z-dn.net/?f=a_n%3D8%2B2n)
In the options below, the only correct answer is option D. so, we can write nth term as: ![d(n) = 8 + 2n\: for\: n > 1](https://tex.z-dn.net/?f=d%28n%29%20%3D%208%20%2B%202n%5C%3A%20for%5C%3A%20n%20%3E%201)
So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is ![\mathbf{d(n)=8+2n\:for\:n>1}](https://tex.z-dn.net/?f=%5Cmathbf%7Bd%28n%29%3D8%2B2n%5C%3Afor%5C%3An%3E1%7D)
Option D is correct option