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3. Graph the arithmetic sequence an = –4, –1, 2, 5, 8, …

 

a. What is the 8th term in the sequence?

 

 

b. What is the recursive formula for this sequence?

 

 

c.  What is the explicit formula for the nth term?  How does this formula relate to the slope intercept form of a linear equation?

 Mar 12, 2019
 #1
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3a.

 

an = a1 + (n - 1) d.

a8 = -4 + 7(3) = 17

 

Therefore the 8th term of the sequence is 17.

 Mar 12, 2019
 #2
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3b.

 

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

 

Because the next term is always greater than the last term by 3.

 Mar 12, 2019
 #3
avatar+7709 
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\(\text{Explicit formula: } a_n = 3n - 7\).

If we plot the graph of \(a_n\) against \(n\) of this explicit formula, we get a straight line with slope = 3 and y-intercept = -7. If we plug in 1,2,3,..., we get the corresponding term of the sequence.

 Mar 12, 2019

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