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Georgia [21]
1 year ago
15

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

tively.
Mathematics
1 answer:
vova2212 [387]1 year ago
5 0

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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(03.01 LC)
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  • Perpendicular=P=4
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Hypotenuse be H

Apply Pythagorean theorem

\\ \tt\hookrightarrow H^2=P^2+B^2

\\ \tt\hookrightarrow H^2=4^2+4^2

\\ \tt\hookrightarrow H^2=32

\\ \tt\hookrightarrow H=\sqrt{32}

\\ \tt\hookrightarrow H=5.8units

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4 0
3 years ago
Solve the following system of equations using elimination (Do not multipy)
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eliminating y from both of the equations and adding the rest of the terms
we get,
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    dividing 8 on both sides
    x = 2
Substituting the value of x in equation 1
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2) 
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      3x - 4y = 5 --> equation 2
eliminating x from both equations and adding the rest of the terms
 we get,
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Substituting the value of y in the equation 1
    -3x - 3(-2) =9
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Step-by-step explanation:

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