Question

What is the common ratio of the geometric sequence whose first term
is 27 and fourth term is 64?
(1) 3/4
(3) 4/3
(3) 64/81
(4) 37/3

Answer 1

$a_1=27;\ a_4=64\\\\a_4:a_1=d^3\\\\subtitue\\\\d^3=64:27\\\\d^3=\dfrac{64}{27}\\\\d=\sqrt[3]{\dfrac{64}{27}}\\\\d=\dfrac{\sqrt[3]{64}}{\sqrt[3]{27}}\\\\d=\dfrac{4}{3}\\\\Answer:\boxed{(3)\ \frac{4}{3}}$

Answer 2

The common ratio of the geometric sequence whose first term

is 27 and fourth term is 64 would be 4/3. so option B is correct.

What is  a geometric sequence and how to find its nth terms?

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

a, ar, ar^2, ar^3,

Thus, the nth term of such sequence would be  T_n = ar^{n-1} (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

a1 = 27

a4 = 64

We know that  a4 : a1 = d³

64 : 27 = d³

d³ = 64/ 27

Taking cube root on both side, we get;

d = 4/3

therefore, The common ratio of the geometric sequence whose first term

is 27 and fourth term is 64 would be 4/3. so option B is correct.

Learn more about geometric sequence here:

https://brainly.com/question/2735005

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