Answer:
a) [tex]a_n=5\,\,(2)^{n-1}[/tex]
b) [tex]b_n=100\,\,(\frac{1}{2} )^{n-1}[/tex]
c) [tex]c_n=160\,\,(-\frac{1}{2} )^{n-1}[/tex]
Step-by-step explanation:
a) Geometric sequence with first term 5 and common ratio 2, where the nth term can be calculated via:
[tex]a_n=5\,\,(2)^{n-1}[/tex]
The first five terms are: [tex]a_1=5;\,\,\,a_2=10;\,\,\,a_3=20; \,\,\,a_4=40;\,\,\,a_5=80[/tex]
b) Geometric sequence with first term 100 and common ratio 1/2, where the nth term can be calculated via:
[tex]b_n=100\,\,(\frac{1}{2} )^{n-1}[/tex]
The first five terms are: [tex]a_1=100;\,\,\,a_2=50;\,\,\,a_3=25; \,\,\,a_4=12.5;\,\,\,a_5=6.25[/tex]
c) Geometric sequence with first term 160 and common ratio -1/2, where the nth term can be calculated via:
[tex]c_n=160\,\,(-\frac{1}{2} )^{n-1}[/tex]
The first five terms are: [tex]a_1=160;\,\,\,a_2=-80;\,\,\,a_3=40; \,\,\,a_4=-20;\,\,\,a_5=10[/tex]
