Answer:
If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is [tex]\mathbf{d(n)=8+2n\:for\:n>1}[/tex]
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: [tex]a_n=a_1+(n-1)d[/tex]
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:
[tex]a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n[/tex]
So, nth term is: [tex]a_n=8+2n[/tex]
In the options below, the only correct answer is option D. so, we can write nth term as: [tex]d(n) = 8 + 2n\: for\: n > 1[/tex]
So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is [tex]\mathbf{d(n)=8+2n\:for\:n>1}[/tex]
Option D is correct option
