Find an explicit formula for the following sequence, an which starts with a1=2/3. 2/3,3/4,4/5,5/6,…

Mathematics

1 answer:

Flura [38]2 years ago

6 0

Answer:

Step-by-step explanation:

a1=2/3

sequence is 2/3,3/4,4/5,...

for numerator a1=2

d=3-2=1

numerator of nth term=a1+(n-1)d=2+(n-1)×1=2+n-1=n+1

denominator = 1 more than numerator=n+1+1=n+2

so an=(n+1)/(n+2)

or for denominator a1=3,d=4-3=1

denominator of nth term=3+(n-1)×1=3+n-1=n+2

an=(n+1)/(n+2)

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Find the percent of the area under the density curve where x is more than 3. <br>

Gekata [30.6K]

Answer:

The percent of the area under the density curve where $x$ is more that 3 is 25 %.

Step-by-step explanation:

Since the density curve is a linear function, the area under the curve can be calculated by the geometric formula for a triangle, defined by the following expression:

$A = \frac{1}{2}\cdot (x_{f} - x_{o})\cdot (y_{f}-y_{o})$ (1)

Where:

$A$ - Area, in square units.

$x_{f} - x_{o}$ - Base of the triangle, in units.

$y_{f} - y_{o}$ - Height of the triangle, in units.

The percent of the area is the ratio of triangle areas under the density curve multiplied by 100 per cent, that is:

$x = \frac{\frac{1}{2}\cdot (5-3)\cdot (0.25) }{\frac{1}{2}\cdot (5-1)\cdot (0.5) }\times 100\,\%$

$x = 25\,\%$

The percent of the area under the density curve where $x$ is more that 3 is 25 %.

7 0

2 years ago

Determine the sum of the arithmetic series: 5+18 +31 +44 + ... 161.

Finger [1]

Answer:

1079

Step-by-step explanation:

Hello,

18-5 = 13

31-18=13

44-31=13

161=5+13*12

So we need to compute

$\displaystyle \sum_{k=0}^{k=12} \ {(5+13k)}\\\\=\sum_{k=0}^{k=12} \ {(5)} + 13\sum_{k=1}^{k=12} \ {(k)}\\\\=13*5+13*\dfrac{12*13}{2}\\\\=65+13*13*6\\\\=65+1014\\\\=1079$