Question

Not geometric
0. What is the 10th term of the sequence 64, 16, 4, ....

Answer 1

10th term of the sequence 64,16,4... = 1/4096

Explanation:

Points to remember

nth term of GP is given by.

Tₙ = ar⁽ⁿ⁻¹⁾

Where r is the common ratio and a is the first term

To find the 10th term of given GP

It is given that,

64, 16, 4,......

a = 64 and 6 = 1/4 Here

T₁₀ = ar⁽ⁿ⁻¹⁾

= 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)

= 4³/4⁹ = 1/4⁶ = 1/4096

Answer 2

`(1)/(4096)`

Explanation:

To solve this we are using the formula for the nth term of a geometric sequence:

`a_n=a_1r^(n-1)`

where

`a_1` is the first term

`r` is the common ratio

`n` is the position of the term in the sequence

The common ratio is just the current term divided by the previous term in the sequence, so
`r=(16)/(64) =(4)/(16) =(1)/(4)`. We can infer from our sequence that its first term is 64, so
`a_1=64`.

Replacing values

`a_n=a_1r^(n-1)`

`a_n=64((1)/(4) )^(n-1)`

We want to find the 10th term, so the position of the term in the sequence is
`n=10`.

Replacing values

`a_n=64((1)/(4) )^(n-1)`

`a_(10)=64((1)/(4) )^(10-1)`

`a_(10)=64((1)/(4) )^(9)`

`a_(10)=(1)/(4096)`

We can conclude that the 10th term of the sequence is
`(1)/(4096)`