Answer:
Six terms of this series will be (-3), (-4.5), (-6.75), (-10.125), (-15.1875), (-22.78125)
Step-by-step explanation:
We have to find the six terms of a geometric series with first term = -3 and common ratio r = 1.5
The explicit form of a geometric series is represented by
[tex]T_{n}=a(r)^{n-1}[/tex]
[tex]T_{1}=(-3)[/tex]
[tex]T_{2}=(-3)(1.5)^{2-1}[/tex]
= (-3)(1.5)
= -4.5
[tex]T_{3}=(-3)(1.5)^{3-1}[/tex]
= (-3)(1.5)²
= (-3)(2.25)
= -6.75
[tex]T_{4}=(-3)(1.5)^{4-1}[/tex]
= (-3)(1.5)³
= -10.125
[tex]T_{5}=(-3)(1.5)^{5-1}[/tex]
= [tex](-3)(1.5)^{4}[/tex]
= (-3)(5.0625)
= -15.1875
[tex]T_{6}=(-3)(1.5)^{6-1}[/tex]
= [tex](-3)(1.5)^{5}[/tex]
= (-3)(7.59375)
= -22.78125
Therefore, Six terms of this series will be (-3), (-4.5), (-6.75), (-10.125), (-15.1875), (-22.78125)
