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inessss [21]
3 years ago
7

After the first term in a sequence, the ratio of each term to the preceding term is r. If the first term is a, what is the third

term?
Mathematics
1 answer:
irinina [24]3 years ago
7 0

Answer:

The 3rd term is

ar^2

Step-by-step explanation:

From the given information, the first term of the sequence is

a_1=a

The common ratio of the sequence is

r

The explicit formula for a geometric sequence is :

a_n=a_1(r^{n-1})

To find the third term, we put n=3 to get:

a_n=a(r^{3-1})

This simplifies to:

a_3=ar^2

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If(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers​
seraphim [82]

Answer:

  • a = 4/3 and b = 0

============================

<h2>Given expression:</h2>

\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}

<h2>Simplify it in steps:</h2>

<h3>Step 1</h3>

Bring both fractions into common denominator:

\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}

<h3>Step 2</h3>

Simplify:

\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =

\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =

\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =

\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =

\dfrac{4\sqrt{14} }{7-4} =

\dfrac{4}{3}  \sqrt{14} }

<h3>Step 3</h3>

Compare the result with given expression to get:

  • a = 4/3 and b = 0

4 0
2 years ago
Help me please please
tatyana61 [14]

Answer:

6.91 times 6.91 equals 47.7481

47.7481 times π equals 150.005080183

to the second digit this is

150.01

5 0
3 years ago
Read 2 more answers
Calculate the area of the given quadrilaterals.​
nadya68 [22]

Answer:

dissect the trapezium into a square and triangle. since the triangle is a right angled one the base is 17-7=10cm

the height is found using Pythagorean theorem to be 24cm i.e 26²=x²+10²,x=√(676-100),x=√576,x=24cn

area of trapezium is (1/2)(a+b)h

a is the shorter side and b the longer side

(1/2)*(7+17)24

=288cm²

3 0
2 years ago
Multiply. (-5 5/8) • (-2 1/3) What is the product?​
lions [1.4K]

Answer:

105/8 = 13 1/8 = 13.125

Step-by-step explanation:

The first step is to turn the (-5 5/8) into a mixed number. The mixed number you should be getting is - 45/8. The second step is to convert the (-2 1/3) into a mixed number as well, your second mixed number should be -7/3. Next multiply the two fractions, - 45/8 x (-7/3) = 315/24.

We can simplify 315/24 by dividing by 3, so you'll divide 315 divided by 3 and 24 divided by 3 and you should get ... 105/8. So 105/ 8 is equal to

13 1/8. If you need this fraction in decimal form it is 13.125.

6 0
10 months ago
The diameter of a circle is 6 units. What is the radius of the circle?
KengaRu [80]

Answer:

3

Step-by-step explanation:

The radius is half of the diameter so 6/2 is 3

3 0
2 years ago
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