Respuesta :
Answer:
The seventh term of a G.P is
[tex]t_{7} = 33,097.211[/tex]
Step-by-step explanation:
step(i):-
Given the second term of a G.P is '4'
The general term of nth term is
[tex]t_{n} = ar^{n-1}[/tex]
[tex]t_{4} = ar^{4-1} =4[/tex]
[tex]ar^{3} =4[/tex] …(i)
Also Given the fifth term of a G.P is '81'
[tex]t_{5} = ar^{5-1} =81[/tex]
[tex]ar^{4} =81[/tex] …(ii)
Step(ii):-
Dividing the equation (ii) divided by (i)
[tex]\frac{ar^{4} }{ar^{3} } = \frac{81}{4}[/tex]
cancellation ' a' and 'r' terms , we get
[tex]r = \frac{81}{4}=20.25[/tex]
substituting 'r' Value in equation (i), we get
[tex]ar^{3} =4[/tex]
[tex]a(\frac{81}{4}) ^{3} =4[/tex]
[tex]a = \frac{4X4X4X4}{(81)^{3} }= \frac{256}{531,441}[/tex]
a = 0.00048
Step(iii):-
The seventh term of G.P
The general term of nth term is
[tex]t_{n} = ar^{n-1}[/tex]
[tex]t_{7} = (0.00048)(20.25)^{7-1}[/tex]
[tex]t_{7} = (0.00048)(20.25)^{6}= 33,097.211[/tex]
