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Consider the arithmetic sequence in which a1 = 6 and a14 = 97

a. Determine the rule for the sequence, and explain your reasoning.

b. Write an explicit equation in y=mx+b form to model the sequence. Show how you derived this equation. 

c. Explain the meanings of the y-intercept and the slope of the equation with respect to the sequence.

d. What is the value of the 28th term of the sequence? Explain how you determined it.

 Jan 5, 2021

Best Answer 

 #1
avatar+412 
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a14-a1 is 91, so the next term will always be 91/(14-1) more than the last, or 7 more.

a) a rule would be a(x)=6+7(x-1)

b) If we use the x axis as the a-number, we get that for every time we move over 1 x, the y increases by 7. This leads to a slope of 7. so we have y=7x+b. Plugging in the above examples a1=6 and a14=97, we get that the full equation should be y=7x-1.

c)The slope is how much the amount changes each time the a-number is increased by one. The y-intercept is the 0th number,-1.

d) using our rule, 6+7*27 is 6+189 or 195.

 Jan 5, 2021
 #1
avatar+412 
+2
Best Answer

a14-a1 is 91, so the next term will always be 91/(14-1) more than the last, or 7 more.

a) a rule would be a(x)=6+7(x-1)

b) If we use the x axis as the a-number, we get that for every time we move over 1 x, the y increases by 7. This leads to a slope of 7. so we have y=7x+b. Plugging in the above examples a1=6 and a14=97, we get that the full equation should be y=7x-1.

c)The slope is how much the amount changes each time the a-number is increased by one. The y-intercept is the 0th number,-1.

d) using our rule, 6+7*27 is 6+189 or 195.

MooMooooMooM Jan 5, 2021

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