Question

Find an explicit function rule for the sequence 5,11,17,23,.... Use the formula a(n) = a(n-1)d and simplify fully.

Answer 1

For this problem, we know d = 6 because (11 - 5) = (17 - 11) = (23 - 17) = 6
Now, we have to use the formula:
$a_{n} = a_{1} + (n-1)d$
For this problem, d = 6 and a(base1) is 5, so plug it in like this:
$a_{n} = 5 + (n - 1)(6)$
To simplify, all you have to do is distribute the six and reduce like so:
$a_{n} = 5 + ((6*n)-(6*1)) \\ a_{n}=5 + 6n - 6 \\ a_{n} = 6n-1$

So, here's your answer:
$a_{n} = 6n-1$

Hope this helps!

Answer 2

Answer:

an = 3 + (n - 1)6

Step-by-step explanation:

Just did it