Mathematics: Consider the arithmetic sequence: 10, 12, 14, 16, ... If n is an integer, which of these functions generate the sequence? Choose all answers that apply: a(n) = 16 + 3n for n 2-2 A b(n) = 14 + 2n for n -1 c(n) = 10 + 3n for n 0 Dd(n) = 8 + 2n for n 1

Consider the arithmetic sequence: 10, 12, 14, 16, - id1012141610614355, cpcoolestkid4

emrecaga1992

17.03.2022

If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n1}$

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

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:

$a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n$

So, nth term is: a_n=8+2n

In the options below, the only correct answer is option D. so, we can write nth term as: $d(n) = 8 + 2n\: for\: n 1$

So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n1}$

Option D is correct option

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