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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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Answer:

16/25

Step-by-step explanation:

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Answer:

Step-by-step explanation:

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S=20

A=\sqrt{s(s-a)(s-b)(s-c)}

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A=\sqrt{(20)(3)(12)(5)}

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3 years ago
please solve the question and show your work find the missing number in 34x =0 show how u got your answer and write full explana
Anastaziya [24]
34x=0
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X=0/34
Then you solve for x
X=0
Hope this helps!
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Step-by-step explanation:

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