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3 years ago

Which expression is equivalent to…

Mathematics

1 answer:

kompoz [17]3 years ago

6 0

Answer:

Step-by-step explanation:

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Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

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1 year ago

What is the slope for y=0.5x+10

laila [671]

Answer: the answer is 0.5

Step-by-step explanation:

Y=mx+b mx= slope b= y intercept

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2 years ago

Please help!! What is the slope of the line?

Usimov [2.4K]

Do you have A picture of the line?

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3 years ago

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What is the range and domain

mr_godi [17]

Answer:

domain is 0 to infinity and range is 5 to infinity

Step-by-step explanation:

x is domain and y is range

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Does the given value make the inequality true? x + 9 > 21, when x = 15

Verizon [17]

Answer:

yes, the inequality is true.

Step-by-step explanation:

15 + 9 = 24

24 > 21

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3 years ago