Question

Ô Use the sequence below to complete each task. 4, -6, -16, -26, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. C. Find the 9th term (a.)

Answer 1

b) The sequence seems to respond to this relation:

$a_n=a_{n-1}-10_{}$

a) The common difference is d=-10:

$a_2-a_1=-6-4=-10$

We can generalize the sequence also referring it to the first term:

$\begin{gathered} a_1=4 \\ a_2=4-10=-6 \\ a_3=-6-10=4-10-10=4-2\cdot10=-16 \\ a_n=4-(n-1)\cdot10 \end{gathered}$

We can apply this to calculate a9:

$a_9=4-(9-1)\cdot10=4-8\cdot10=4-80=-76$

c) The 9th term is -76.