Answer
a. The first 5 terms are 6, -3, 1.5, -.75, .375.
b. The common difference is -.5.
c. To graph the first five terms let n represent the x axis and each term represent a value on the y-axis. Plot the corresponding points on a coordinate grid.
Work Step by Step
a. The sequence is represented by $a_{n} = 6(-.5)^{n-1}$ To find the first term plug in n = 1 and solve: $a_{n} = 6(-.5)^{n-1}$ $a_{n} 6(-.5)^{1-1}$ $a_{n} = 6(-.5)^{0}$ = 6$\times$ 1 = 6. 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.
