Question

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thank you
The graph represents the first three terms in an arithmetic sequence.

a. Find the explicit expression for this sequence




b. Find the recursive expression for this sequence



c. What is the 15th term?

Answer 1

a)
`a_n=3n-2`

b)
`a_n=a_(n-1)+3`

c)
`a_(15)=43`

Explanation:

Arithmetic Sequences

In an arithmetic sequence, each number is obtained as the previous number plus or minus a constant value known as the common difference. The general term for an arithmetic sequence is

`a_n=a_1+(n-1)r\ ,\ n\geq 1`

where a_1 is the first term, r the common difference and n the number of terms

If we wanted to express the sequence in the recursive form, we only need to write each term as a function of the previous term.

`a_n=a_(n-1)+r`

a) We can see in the graph the following sequence: 1, 4, 7 where clearly each term equals the previous term plus 3 (the common difference). So our general term is

`a_n=1+3(n-1)`

`a_n=1+3n-3`

`a_n=3n-2`

b) The recursive expression is

`a_n=a_(n-1)+3`

c) To determine
`a_(15)`, we use n=15 in the general term

`a{15}=3(15)-2=45-2`

`a_(15)=43`