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2 years ago

In the geometric sequence below, what is the common ratio? Sequence: 64,16,4,1

Mathematics

1 answer:

Elanso [62]2 years ago

4 0

9514 1404 393

Answer:

1/4

Step-by-step explanation:

The common ratio is the ratio of successive terms:

16/64 = 4/16 = 1/4

The common ratio is 1/4.

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What is the value of b in the equation (y Superscript b Baseline) Superscript 4 Baseline = StartFraction 1 Over y Superscript 24

shusha [124]

The value of b is -6.

Explanation:

The expression is $\left(y^{b}\right)^{4}=\frac{1}{y^{24}}$

To determine the value of b, we shall solve the expression.

Applying exponent rule, $\left(a^{b}\right)^{c}=a^{b c}$ , we get,

$y^{4b}=\frac{1}{y^{24}}$

Applying exponent rule, $\frac{1}{a^{b}}=a^{-b}$ , we have,

$y^{4b}=y^{-24}$

The expression is of the form, $a^{f(x)}=a^{g(x)}$ then $f(x)=g(x)$

Applying this rule, we get,

$4b=-24$

Dividing both sides by 4, we have,

$b=-6$

Hence, the value of b is -6.

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