Question

The first term of a geometric sequence is 2 and the common ratio is 4. What is the 6th term of the sequence?

Answer 1

`a_(6) = 2048`

Step-by-step explanation

The general term of a geometric sequence is given by,

`a_(n) = a_(1) ( {r})^(n - 1)`

The first term of the geometric sequence is 2

`a_(1) =2`

The common ratio is 4. This means r=5.

The nth term of the sequence is

`a_(n) = 2 ( {4})^(n - 1)`

The 6th term is

`a_(6) = 2 ( {4})^(6 - 1)`

`a_(6) = 2 ( {4})^(5)`

`a_(6) = 2048`

Answer 2

Answer: 2048

Step-by-step explanation:

Tn = arⁿ⁻¹

T6 = ar⁶⁻¹

T6 = ar⁵

T6 = 2*4⁵

T6= 2048