Question

The second term of a GP is 4, the fifth term is 81. Find the seventh term

Answer 1

Answer:

The seventh term of a G.P is

$t_{7} = 33,097.211$

Step-by-step explanation:

step(i):-

Given the second term of a G.P is '4'

The general term of nth term is

$t_{n} = ar^{n-1}$

$t_{4} = ar^{4-1} =4$  

$ar^{3} =4$ …(i)    

Also Given the fifth term of a G.P is '81'

$t_{5} = ar^{5-1} =81$

$ar^{4} =81$  …(ii)      

Step(ii):-

Dividing the equation (ii) divided by (i)

$\frac{ar^{4} }{ar^{3} } = \frac{81}{4}$

cancellation ' a' and 'r' terms , we get

$r = \frac{81}{4}=20.25$

substituting 'r' Value in equation (i), we get

$ar^{3} =4$

$a(\frac{81}{4}) ^{3} =4$  

$a = \frac{4X4X4X4}{(81)^{3} }= \frac{256}{531,441}$

a = 0.00048

Step(iii):-

The seventh term of G.P

The general term of nth term is

$t_{n} = ar^{n-1}$

$t_{7} = (0.00048)(20.25)^{7-1}$

$t_{7} = (0.00048)(20.25)^{6}= 33,097.211$