+86 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.
+538 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.
+538 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.
