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2 years ago

What is the 13th term of the geometric sequence 4, 12, 36, 108, ...?

Mathematics

1 answer:

bogdanovich [222]2 years ago

7 0

Answer: 2,125,764

Step-by-step explanation:

You can use the equation y=ar^n-1 to find the 13th term where a is the starting term, r is the common ratio, and n is the nth term

The next number is 12/4=3 times greater than the first. So if this sequence is a geometric one, then the next term must be 12*3=36. This is true, and the next term must be 36*3=108, which is also true. Therefore this sequence is a geometric one and its common ratio is 3. Therefore the equation is:

y=4*3^(n-1)

Substitute 13 for n:

y=4*3^(13-1)

y=4*3^12

y=2125764

Therefore, the 13th term of this geometric sequence is 2,125,764

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Step-by-step explanation:

Dividing:

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4 years ago

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Step-by-step explanation:

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3 years ago

Read 2 more answers

in parallelogram ABCD, AC is diagonal, the measure <ABC is 40°, and the measure of <ACD IS 57°. what is the measure of &lt

Nutka1998 [239]

Answer: $\angle CAD = 83^\circ$ Option D

Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD

$\angle ABC=40^\circ$

As, we know that opposite angles of parallelogram are equal

Therefore,

$\angle ABC =\angle ADC =40^\circ$

Now, in triangle ADC

We know that sum of all the angles of a triangle is $=180^\circ$

$\angle ACD +\angle ADC +\angle DAC =180^\circ$

$57^\circ +40^\circ +\angle DAC =180^\circ$

$97^\circ + \angle DAC = 180^\circ$

Subtracting 97 from both sides we get

$\angle DAC = 180^\circ - 97^\circ$

$\angle DAC = 83^\circ$

Measure of $\angle CAD = 83^\circ$

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3 years ago

Solve the inequality and graph the solution set on a number line. Express the solution set in both set-builder and interval not

shusha [124]

-8 < x -3 < 1
we have two inequations:
* -8<x-3 and -8+3<x-3+3 or -5 < x or x>-5
* x-3<1 or x-3+3<1+3 and we have x<4
For all cases we have -5<x<4
or interval notations: x∈(-5;4)
have fun

8 0

3 years ago