Write an explicit and a recursive formula for each sequence. 2,4,6,8,10

1 answer:

8 0

There is already a derived formula for this type of series. This is arithmetic series. It consists of a group of numbers arranged to together with a common difference. For this series, the common difference is 2. See the pattern: 4-2 = 2, 6 - 4 = 2, 8 - 6 = 2, 10- 8=2

The formula for an arithmetic series is

An = A1 + (n-1)d

where An is the nth term of the series, A1 is the 1st term, n is the number of terms and d is the common difference.

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In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each poin

Korolek [52]

Step-by-step explanation:

We have cartisean points. We are trying to find polar points.

We can find r by applying the pythagorean theorem to the x value and y values.

$r {}^{2} = {x}^{2} + {y}^{2}$

And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.

$\tan(x) = \frac{y}{x}$