Question

Find the term named in the problem

2,4,8,16
Find a11

Answer 1

The 11th term of the sequence is
`a_(11)=2048`

Step-by-step explanation:

The sequence is
`2,4,8,16`

We need to find the 11th term of the sequence.

First, let us determine the common ratio of the sequence.

`r=(4)/(2) =2`

`r=(8)/(4) =2`

`r=(16)/(8) =2`

Thus, the common ratio of the sequence is
`r=2`

Since, the sequence follows geometric progression.

The general formula for GP is

`a_n=ar^(n-1)`

Substituting
`n=11`,
`r=2` and
`a=1` we have,

`a_(11)=2(2)^(11-1)`

`=2(2)^(10)`

`=2(1024)`

`=2048`

Thus, the 11th term of the sequence is
`a_(11)=2048`