Answer:
the common ratio is 5/8 for the given sequence.
Would you like to suggest the next number?
Step-by-step explanation:
Answer:
a) The sequence is geometric
b) [tex]t_n=5\times \left (\frac{8}{5} \right )^{n-1}[/tex]
c) Seventh term = 83.88608
Step-by-step explanation:
If it is an arithmetic progression common difference will be same,
8 - 5 = 3
12.8 - 8 = 4.8
Since common difference is not same the numbers are not arithmetic.
If it is an geometric progression common ration will be same,
[tex]\frac{8}{5}\\\\\frac{12.8}{8}=\frac{8}{5}\\\\\frac{20.48}{12.8}=\frac{8}{5}[/tex]
Since common ratio is same the numbers are geometric.
b) General term of GP is given by
[tex]t_n=ar^{n-1}=5\times \left (\frac{8}{5} \right )^{n-1}\\\\t_n=5\times \left (\frac{8}{5} \right )^{n-1}[/tex]
c) Seventh term means n = 7
[tex]t_7=5\times \left (\frac{8}{5} \right )^{7-1}=5\times \left (\frac{8}{5} \right )^{6}=83.88608[/tex]
Seventh term = 83.88608
