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Komok [63]
3 years ago
12

A sequence can be represented by the formula t(n)=6; t(n+1)=3*t(n). write the first 4 terms of the sequence. what would be an ex

plicit equation for this same sequence?
Mathematics
1 answer:
Kamila [148]3 years ago
8 0

Answer:

Learn how to find explicit formulas for arithmetic sequences. For example, find an explicit formula for 3, 5, 7,... ... CCSS Math: HSF. ... plug in the number of the term we are interested in, and we will get the value of that term. ... Writing explicit formulas ... Check out, for example, the following calculations of the first few terms.

Step-by-step explanation:...

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Apply Newton’s method to estimate the solution of x3 − x − 1 = 0 by taking x1 = 1 and finding the least n such that xn and xn +
ss7ja [257]

Solution :

Given

$f(x)=x^3-x-1, x_1=1$

$f'(x)=3x^2-1$

Let the initial approximation is $x_1 =1$

So by Newton's method, we get

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)},n=1,2,...$

$x_2=x_1-\frac{f(x_1)}{f'(x_1)}=1-\frac{1^3-1-1}{3(1)^2-1}=1.5$

$x_3=1.5-\frac{(1.5)^3-1.5-1}{3(1.5)^2-1}=1.34782608$

$x_4=1.34782608-\frac{(1.34782608)^3-1.34782608-1}{3(1.34782608)^2-1}=1.32520039$

$x_5=1.32520039-\frac{(1.32520039)^3-1.32520039-1}{3(1.32520039)^2-1}=1.32471817$

$x_6=1.32471817-\frac{(1.32471817)^3-1.32471817-1}{3(1.32471817)^2-1}=1.32471795$

$x_5 \approx x_6$ are identical up to eight decimal places.

The approximate real root is x ≈ 1.32471795

∴ x = 1.32471795

4 0
3 years ago
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8 0
3 years ago
Write the equation of a line in slope intercept form of a line that has a slope of 5 and a y
xenn [34]

Answer: y=5x-8

Step-by-step explanation: slope intercept form is y=mx+b. M stands for the slope and B stands for the y-intercept. You just need to input what the question is telling you.

8 0
3 years ago
Which type of triangle, if any, has side lengths of 11, 15, and 25?
abruzzese [7]

Answer:

Scalene triangle

Step-by-step explanation:

An equilateral triangle has 3 equal sides.

An isosceles triangle has 2 equal sides.

A scalene triangle has no equal sides.

4 0
3 years ago
Read 2 more answers
The length of a rectangle is 3 feet longer than the width. The perimeter is 30 feet. Find the length and width of the rectangle.
barxatty [35]

Answer:

do you mean height, because then the answer would be a length of 9 and height of 6

Step-by-step explanation:

9+9=18

6+6=12

18+12=30

5 0
3 years ago
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