Respuesta :
Answer:
(n×4)
Step-by-step explanation:
Divide the 2nd term by the first to find the ratio which is also n.
Answer:
n=5.
Step-by-step explanation:
The given geometric series is
1+ 4 +16 + 64 + 256
In the given G.P. the number of terms is 5 and n represents the number of terms in a G.P. So, n=5.
Alternate method:
Here the first term is 1 and the common ratio is
[tex]r=\dfrac{a_2}{a_1}=\dfrac{4}{1}=4[/tex]
The nth term of a G.P. is
[tex]a_n=ar^{n-1}[/tex]
where, a is first term and r is common ratio.
Substitute a=1, an=256 and r=4 in the above formula.
[tex]256=(1)(4)^{n-1}[/tex]
[tex]4^4=4^{n-1}[/tex]
On comparing both sides we get
[tex]4=n-1[/tex]
Add 1 on both sides.
[tex]5=n[/tex]
Therefore, the value of n is 5.
