Question

What is the recursive rule for a n=3n+5

Answer 1

Answer:

$\left \{ {{a_{1} =8} \atop {a_{n} =a_{n-1} +3}} \right.$

Step-by-step explanation:

The given rule is

$a_{n}=3n+5$

If we substitute $n=1, n=2, n=3, n=4,..$

The sequence would be

$a_{1}=3(1)+5=3+5=8\\a_{2}=3(2)+5=6+5=11\\a_{3}=3(3)+5=9+5=14\\a_{4}=3(4)+5=12+5=17$

As you can observe, the arithmetic sequence has a difference of 3, that is, adding 3 units to one term, we obtain the next one. Now, we can use this rule to right a recursive rule.

First, we have to write the first term

$a_{1}= 8$

Then, we write the patter to obtain the next terms, which is adding 3 units, so

$a_{n}=a_{n-1}+3$

Therefore, the recursive rule for $a_{n}=3n+5$ is

$\left \{ {{a_{1} =8} \atop {a_{n} =a_{n-1} +3}} \right.$

Answer 2

Answer:

i believe the answer is -2n=5

Step-by-step explanation:you subtract the 3n with the n and -2n cant go into 5