Answer:
S = {-6.25, -7.813, -9.766, -12.207, -15.259 and -19.703}
Step-by-step explanation:
The first term (a₁) and the common ration (r) of a finite sequence are provided.
a₁ = -6.25
r = 1.25
The nth term of a geometric sequence is:
[tex]T_{n}=a_{1}\cdot r^{n-1}[/tex]
Compute the first six terms as follows:
[tex]T_{1}=a_{1}\cdot r^{1-1}=a_{1}=-6.25\\\\T_{2}=a_{1}\cdot r^{2-1}=-6.25\times 1.25=-7.8125\approx -7.813\\\\T_{3}=a_{1}\cdot r^{3-1}=-6.25\times (1.25)^{2}=-9.765625\approx -9.766\\\\T_{4}=a_{1}\cdot r^{4-1}=-6.25\times (1.25)^{3}=-12.20703\approx -12.207\\\\T_{5}=a_{1}\cdot r^{5-1}=-6.25\times (1.25)^{4}=-15.25879\approx -15.259\\\\T_{6}=a_{1}\cdot r^{6-1}=-6.25\times (1.25)^{5}=-19.07349\approx -19.073[/tex]
Thus, the six terms of a finite sequence are:
S = {-6.25, -7.813, -9.766, -12.207, -15.259 and -19.703}
