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Nastasia [14]
3 years ago
9

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

Mathematics
1 answer:
kramer3 years ago
5 0

Given:

The sequence is:

16,80,400,...

To find:

The 6th term of the given sequence.

Solution:

We have,

16,80,400,...

Here, the first term is:

a=16

The ratio between consecutive terms are:

\dfrac{80}{16}=5

\dfrac{400}{80}=5

The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.

The nth term of a geometric sequence is:

a_n=a(r)^{n-1}

Where, a is the first term and r is the common ratio.

Substitute a=16,r=5,n=6 to get the 6th term.

a_6=16(5)^{6-1}

a_6=16(5)^{5}

a_6=16(3125)

a_6=50000

Therefore, the 6th term of the given sequence is 50000.

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2 years ago
Answer two questions about Equations AAA and BBB: \begin{aligned} A.&amp;&amp;\dfrac x4+1&amp;=-3 \\\\ B.&amp;&amp;x+4&amp;=-12
luda_lava [24]

The given equations are as follows

\begin{aligned} A.&&\dfrac x4+1&=-3 \\\\ B.&&x+4&=-12 \end{aligned}

(1) First, multiply both sides of equation A by 4, we have

4\times\left(\frac{x}{4} +1\right)=4\times(-3)

Then, rewrite the left-hand side of the above equation by using the distributive property, we have

4\times\frac{x}{4}+4\times1=4(-3)

\Rightarrow x+4=-12

This is the required equation B.

In this way, first use choice D: Multiply both sides by the same non-zero constant, i.e 4.

Then, apply choice A to solve the equation, i.e using the distributive property to solve the left-hand side of the equation.

(2) In the previous answer, equation B has been derived from equation A, hence, both the equations are equivalent.

As both the equations are the same, so both will have the same solution.

Yes, they have the same solution.

3 0
3 years ago
Can someone please help w/this
Vikentia [17]

The smallest of the 3 interior angles of the triangle is 10 degrees. Note that the diagram is not to scale.

Thus, sin 10 degrees = opp / hyp = 200 m / x

0.1736 = (200 m) / x, or x = (200 m) / 0.1736

= 1152 m (rounded up from 1151.75 m).

4 0
3 years ago
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