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tia_tia [17]
3 years ago
11

Find the series in A.P whose sum to n terms is n*(n+2)​

Mathematics
1 answer:
Lemur [1.5K]3 years ago
3 0

Answer:

3, 5, 7, 9, 11, .........

Step-by-step explanation:

Given

S_{n} = n(n + 2) , then

S₁ = 1(1 + 2) = 1(3) = 3 ⇒ a₁ = 3

S₂ = 2(2 + 2) = 2(4) = 8

S₃ = 3(3 + 2) = 3(5) = 15

Thus

a₂ = S₂ - S₁ = 8 - 3 = 5

a₃ = S₃ - S₂ = 15 - 8 = 7

The first 3 terms are 3, 5, 7

This is an AP with common difference d = 2, then

a₄ = a₃ + 2 = 7 + 2 = 9

a₅ = a₄ + 2 = 9 + 2 = 11

and so on

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Evaluate the given expression 9P6
iogann1982 [59]

Answer:

60480

Step-by-step explanation:

nPr=\frac{n!}{\left(n-r\right)!}\\\\nPr=\frac{9!}{\left(9-6\right)!}=nPr=\frac{9!}{\left3\right!}=\frac{9*8*7*6*5*4*3*2*1}{3*2*1}=60480

8 0
3 years ago
What is the solution of x+8/5x-1>0?
DerKrebs [107]

Answer:

x<-8 or x>1/5

Step-by-step explanation:

\frac{x+8}{5x-1} >0

First we replace > symbol by = sign

\frac{x+8}{5x-1} =0

To solve for x we multiply 5x-1 on both sides

x+8 =0

x=-8

5x-1=0 solve for x

x= 1/5

WE got two values x=-8  and x= 1/5

Now we make a number line and check with each interval

x<-8,  -8<x<1/5,  x>1/5

Pick x= -9 and check with the given inequality

\frac{-9+8}{5(-9)-1} >0

1/46 >0 is true, so x<-8 satisfies our inequality

Pick x= 0 and check with the given inequality

\frac{0+8}{5(0)-1} >0

-8 >0 is false , -8<x<1/5 does not satifies our inequality

Pick x= 2 and check with the given inequality

\frac{2+8}{5(2)-1} >0

10/9>0 is true , x>1/5  satisfies our inequality

3 0
3 years ago
Read 2 more answers
What is the relationship between the two ratios?
antoniya [11.8K]
10/14 = 5/7
30/36 = 5/6

answer
not proportional
4 0
2 years ago
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What is the result of isolating y2 in the equation below? 9x2 + 7y2 = 42
ElenaW [278]
First, move 9x^2 to the right:

7y^2 = 42 - 9x^2

Then, divide 7 on both sides:

y^2 = 6 - 9/7 * x^2
8 0
3 years ago
How much would $100 invested at 8% intrest compounded annually be worth after 15 years? round your answer to the nearest cent. d
frosja888 [35]
Our P = 100, r = .08, n = 1 (annually means once a year), and t = 15.  Filling in accordingly, we have A(t)=100(1+ \frac{.08}{1})^{(1)(15)}.  Simplifying a bit gives us  A(t)=100(1+.08)^{15}  and  A(t)=100(1.08)^{15}.  Raising that number inside the parenthesis to the 15th power gives us  A(t)=100(3.172169114).  Multiplying to finish means that A(t) = $317.22
3 0
3 years ago
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