Question

Which recursive rule can be used to find the bth term of the sequence, an

Answer 1

Answer:

$A\text{ : a}_1\text{ = 9 , a}_n\text{ = a}_{n-1}\text{ + 6}$

Explanation:

Here, we want to get the formula that could be used to represent the rule of the sequence

From the given terms:

4th term is 9 and the 5th term is 15

6th term is 21, 7th is 27 and 8th is 33

What this means is that the difference between each of the terms is 6

Hence, we add 6 to the current term to get the next term

Thus:

$a_n\text{ = a}_{n-1}\text{ + 6}$

Now, to get the first term, we can see that we are 3 differences away from the 3rd term

Hence, the value of the first term will be:

$9-6(3)\text{ = -9}$

Thus, we have the first term as -9