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Which formula can be used to find the nth term in a geometric sequence where
[tex]a1=3 [/tex] and [tex]r=2[/tex]
A. [tex]an=3+2(n-1)[/tex]
B. [tex]an=3(n-1)+2[/tex]
C. [tex]an=3^n^-^1*2[/tex]
D. [tex]an=3*2^n^-^1[/tex]

Respuesta :

ghanami
hello : 
the nth term in a geometric sequence where is ; 
an = a1 ×qn     .... q : common ratio       a1 the first term
exempl : 
C) an  =  2×3^n-1
an =2×3^n ×3^-1
an =(2/3)×3^n
a1 = 2/3  and q= 3
same method for : D

Answer:

an = 3*(2)^(n-1)  ... Option D

Step-by-step explanation:

Given:-

- The two parameters of a geometric sequence are given:-

                                a1 = 3 , r = 2

Find:-

Which formula can be used to find the nth term in a geometric sequence

Solution:-

- A sequence can be expressed in a general form as:

                              a1 , a2 , a3 , a4 , .... an

- For a sequence to be classified as geometric we need two parameters that are first term and common ratio:

                              First term = a1

                              Common ratio = r = a2 / a1 = a3 / a2 = a4/a3 ... = an / an-1

- The given two parameters are:

                               a1 = 3 , r = 2

- The general term in a geometric sequence can be determined from the following formula:

                              an = a1*(r)^( n - 1 )

Where, n = 1 ,2 , 3 , 4 , ... Last term number.

                              an = 3*(2)^(n-1)

                             

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