Question

Trixie is at it again. This time she wants an arithmetic sequence that has a graph with a slope of 22. She also wants t(8)=164 and the 13th term to have a value of 300. Is it possible to create an arithmetic sequence to fit her information? If it is possible, find the equation. If it is not possible, explain why not.

Answer 1

All arithmetic sequences are of the form a, a+d, a+2d, a+3d, etc., so a formula for the the term t(n)=a+(n-1)d where a is the first term (n=1, t(1)=a) and d is the common difference. Therefore t(8)=164=a+7d. And t(13)=a+12d=300. 300-164=5d. 5d=136, d=136/5=27.2, making a=164-7(27.2)=164-190.4=-26.4. t(n)=-26.4+27.2n. The gradient (slope) is (300-164)/(13-8) or (300-164)/(12-7)=27.2 (=d) and not 22. So it is not possible to fit all these conditions.