Answer
a. The first five terms are 2.5, -1.25, .625, -.3125, .15625
b. The common difference is -$\frac{1}{2}$ = -.5
c. To graph the first 5 terms let n represent the x axis and the terms represent points on the y-axis. Plot corresponding points on the x and y axes.
Work Step by Step
a. The sequence is represented by $a_{n} = \frac{5}{2}(-\frac{1}{2})^{n-1}$ To find the first term plug in n = 1 and solve: $a_{n} = \frac{5}{2}(-\frac{1}{2})^{1-1}$ $a_{n} = \frac{5}{2}(-\frac{1}{2})^{0}$ = $ \frac{5}{2}\times \ 1 = \frac{5}{2}$. Repeat for n =2,3,4, and 5.
b. The common ratio is the r value in the formula - the ratio each term is multiplied by. In this case each term is multiplied by -.5 so the common ratio is -.5
c. See above for how to graph the first five terms of the sequence.
