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

Question

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


`a1=3` and
`r=2`
A.
`an=3+2(n-1)`
B.
`an=3(n-1)+2`
C.
`an=3^n^-^1*2`
D.
`an=3*2^n^-^1`

Answer 1

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 2

an = 3*(2)^(n-1) ... Option D

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)