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valkas [14]
3 years ago
12

What is the term-to-term rule for this sequence? 64, 32, 16, 8, 4

Mathematics
1 answer:
just olya [345]3 years ago
4 0

Answer:

a n=1/2 an - 1

Step-by-step explanation:

64,32,16,8,4. is a geometric sequence. this is a sequence where, to get from one term to the next, there is a number that you have to multiply it by. this is the same for all parts of the sequence.

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AP Calculus redo! I know the answer but can't figure out exactly how to get there. Thank you! I want to work through the steps.
Monica [59]
You're approximating

\displaystyle\int_1^5 x^2\,\mathrm dx

with a Riemann sum, which comes in the form

\displaystyle\int_a^b f(x)\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^nf(x_i)\Delta x_i

where x_i are sample points chosen according to some decided-upon rule, and \Delta x_i is the distance between adjacent sample points in the interval.

The simplest way of approximating the definite integral is by partitioning the interval into equally-spaced subintervals, in which case \Delta x=\dfrac{b-a}n, and since [a,b]=[1,5], we have

\Delta x=\dfrac{5-1}n=\dfrac4n

Using the right-endpoint method, we approximate the area under f(x) with rectangles whose heights are determined by their right endpoints. These endpoints are chosen by successively adding the subinterval length to the starting point of the interval of integration.

So if we had n=4 subintervals, we'd split up the interval of integration as

[1,5]=[1,2]\cup[2,3]\cup[3,4]\cup[4,5]

Note that the right endpoints follow a precise pattern of

2=1+\dfrac44
3=1+\dfrac84
4=1+\dfrac{12}4
5=1+\dfrac{16}4

The height of each rectangle is then given by the values above getting squared (since f(x)=x^2). So continuing with the example of n=4, the Riemann sum would be

\displaystyle\sum_{i=1}^4\left(1+\dfrac{4i}4\right)^2\dfrac44

For n=5,

\displaystyle\sum_{i=1}^5\left(1+\dfrac{4i}5\right)^2\dfrac45

and so on, so that the definite integral is given exactly by the infinite sum

\displaystyle\lim_{n\to\infty}\sum_{i=1}^n\left(1+\dfrac{4i}n\right)^2\dfrac4n
4 0
3 years ago
What is the radius of a circle with a circumference of 36(3.14) cm
mart [117]
It should be 18, because despite of 3,14, because that's pi and radius is half of the diameter, so36 divide 2 is 18.
6 0
3 years ago
In a certain year the population of a country reached 321 million. The overall birth rate was births per​ 1000, and the overall
kkurt [141]

Answer:

Then it would stay at 321 million

Step-by-step explanation:

if the birth and death rate is both 1000 then nothing will change. Population wise.

4 0
3 years ago
The scale on a map is 1:500000 two towns are 7cm apart
Eddi Din [679]
7 x 500,000 = 3,500,000.

The towns are 3,500,000 units apart (I don't know what the cm were scale too, sorry.)
7 0
3 years ago
Make 24 using 1,2,2,7
alexdok [17]
7 times 2=14
14 times 2=24
24 times 1=24
5 0
3 years ago
Read 2 more answers
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