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puteri [66]
3 years ago
14

2. Find the common difference and the recursive formula. a. 22, 19, 16, 13, …

Mathematics
1 answer:
Musya8 [376]3 years ago
6 0

Answer:

The common difference d is d = -3

The recursive formula is: \mathbf{a_n=a_{n-1}-3}

Step-by-step explanation:

We need to find the common difference and the recursive formula.

a. 22, 19, 16, 13, …

First we will find common difference

The formula of arithmetic sequence is: a_n=a_1+(n-1)d

where a_n is nth term, a_1 is 1st term and d is the difference

Looking at the sequence we get: a_1=22, a_2=19

Using these values we can find d, the common difference

a_n=a_1+(n-1)d\\put\:n=2, a_2=19, a_1=22\\19=22+(2-1)d\\19=22+d\\d=19-22\\d=-3

So, the common difference d is d = -3

Now, we will find the recursive formula:

The recursive formula is of type: a_n=a_{n-1}+d

We have found common difference d = -3

So, the recursive formula will be:

a_n=a_{n-1}+d\\a_n=a_{n-1}+(-3)\\a_n=a_{n-1}-3

The recursive formula is: \mathbf{a_n=a_{n-1}-3}

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