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9. Use the graph of the sequence to answer the parts.

a. Is the sequence arithmetic, geometric, or neither Explain.

b. Write a recursive formula for the sequence.

c. Write an explicit formula for the sequence.

9 Use The Graph Of The Sequence To Answer The Parts A Is The Sequence Arithmetic Geometric Or Neither Explain B Write A Recursive Formula For The Sequence C Wri class=

Sagot :

MrRoyalidn

The recursive formula for the sequence is T(n+1) = Tn - 3 where T1 = 19 and the explicit formula for the sequence is Tn = 22 - 3n

a. Is the sequence arithmetic, geometric, or neither

On the given graph, we have the following points

19, 16, 13, 10, 7

These points represent the nth term of the sequence

See that the points have a common difference of -3

Hence, the sequence is an arithmetic sequence

b. Write a recursive formula for the sequence.

In (a), we have

T1 = 19

d = -3

So, we have

T2 = T1 + d

This gives

T2 = T1 - 3

Express 2 as 1 + 1

So, we have

T(1+1) = T1 - 3

Express 1 as n

So, we have

T(n+1) = Tn - 3

Hence, the recursive formula for the sequence is T(n+1) = Tn - 3 where T1 = 19

c. Write an explicit formula for the sequence.

In (a), we have

T1 = 19

d = -3

So, we have

Tn = T1 + (n - 1)d

This gives

Tn = 19 + (n - 1) * -3

Evaluate

Tn = 19 + 3 - 3n

Evaluate the sum

Tn = 22 - 3n

Hence, the explicit formula for the sequence is Tn = 22 - 3n

Read more about sequence at:

https://brainly.com/question/7882626

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