Which best describes the relationship between the successive terms in the sequence below? –3.2, 4.8, –7.2, 10.8, …

2 answers:

6 0

Since you are not given the following choices, by analyzing this series, it is a geometric progression because their common ratio is constant. Proofing that
4.8/(-3.2) = -1.5, also
-7.2/(4.8) = -1.5, and also
10.8/(-7.2) = -1.5

taurus [48]3 years ago

5 0

Solution:

we have been asked to find the relationship between the successive terms in the sequence below? –3.2, 4.8, –7.2, 10.8, …

As we can see the given successive terms in the sequence is following a particular pattern as shown below:

$\frac{4.8}{-3.2}=\frac{-7.2}{4.8}=\frac{10.8}{-7.2}=-1.5$

Its following properties of geometric sequence. Because the ratios of the successive terms is constant. So its a geometric progression.

Hence the given successive terms in the sequence is a geometric sequence.

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ANTONII [103]

Megan:
x to the one third power = $x ^{1/3}$
x to the one twelfth power = $x ^{1/12}$

The quantity of x to the one third power, over x to the one twelfth power is:
 $\frac{x ^{1/3}}{x ^{1/12}}$

Since $\frac{ x^{a} }{ x^{b} } = x ^{a-b}$
then $\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12}$

Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4

$\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12} = x^{1/4}$

Julie:
x times x to the second times x to the fifth = x * x² * x⁵

The thirty second root of the quantity of x times x to the second times x to the fifth is
 $\sqrt[32]{x* x^{2} * x^{5} }$

Since $x^{a}* x^{b}= x^{a+b}$
Then $\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }$

Since $\sqrt[n]{x^{m}} = x^{m/n} }$
Then $\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}$

Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.

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