Question

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

Answer 1

Answer:

$\frac{1}{4096}$

Step-by-step 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 $r=\frac{16}{64} =\frac{4}{16} =\frac{1}{4}$. We can infer from our sequence that its first term is 64, so $a_1=64$.

Replacing values

$a_n=a_1r^{n-1}$

$a_n=64(\frac{1}{4} )^{n-1}$

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

Replacing values

$a_n=64(\frac{1}{4} )^{n-1}$

$a_{10}=64(\frac{1}{4} )^{10-1}$

$a_{10}=64(\frac{1}{4} )^{9}$

$a_{10}=\frac{1}{4096}$

We can conclude that the 10th term of the sequence is $\frac{1}{4096}$

Answer 2

Answer:

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

Step-by-step 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