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sergey [27]
3 years ago
15

The formula to find a certain number in an arithmetic sequence is an=a1+d(n−1)an=a1+d(n−1) .

Mathematics
2 answers:
noname [10]3 years ago
5 0

Answer: n=\dfrac{a_n-a_1}{d}+1

Step-by-step explanation:

Given : The formula to find a certain number in an arithmetic sequence is

a_n=a_1+d(n-1), where a_n is the nth term , a_1 is the first term and d is the common difference.

To solve the formula for n , first subtract a_1 from both sides , we get

a_n-a_1=d(n-1)

Now, divide d on both sides , we get

\dfrac{a_n-a_1}{d}=n-1

Now, add 1 to the both sides , we get

\dfrac{a_n-a_1}{d}+1=n

Or

n=\dfrac{a_n-a_1}{d}+1

cluponka [151]3 years ago
4 0
The formula of arithmetic sequence is
an = a₁ + d(n - 1)

Then we need to find the formula to determine n. I reverse the equation so the 'n' will be on the left side.
a₁ + d(n - 1) = an

Then I move all the terms on the left one by one to the right side except n
a₁ + d(n - 1) = an
d(n - 1) = an - a₁
n - 1 = (an - a₁)/d
n = 1 + (an - a₁)/d

This is the formula to solve n
n = 1 + (an - a₁)/d
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Answer:

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Step-by-step explanation:

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Answer:

Suppose the equation that describes the change in water vapor in a cloud (y) with respect to temperature (x): C(x) = x³ - 4x² - 7x + 10

You find the x-intercepts of the cubic equation by finding the roots. Let y be zero:

x³ - 4x² - 7x + 10 = 0

Now, find possible factors of the constant term in the equation: 10. These could be 1, 2, 5, and 10. Suppose we choose 1. We substitute x=1. If the answer is zero, then x=1 is one of the roots.

(1)³ - 4(1)² - 7(1) + 10 = 0

Hence, x=1 or x-1 = 0 is one of the roots. We use this to manipulate the rest of the terms in the original equation, such that you can factor out (x-1). Substitute -x² - 3x² to -4x³ because they are just equal. Same is true for +3x - 10x for -7x:

x³ -x² - 3x²+3x - 10x + 10 = 0

Factor out like terms such that they have a common factor of (x-1) as much as possible.

x³ -x² = x²(x-1)

- 3x²+3x = -3x(x-1)

- 10x + 10 = -10(x-1)

The factored equation is:

x²(x-1)-3x(x-1)-10(x-1) = 0

Factor out (x-1):

(x-1)(x²-3x-10) = 0

Now, we have the quadratic equation left to be solved:x²-3x-10

Use the quadratic formula to find the roots:

x = [-b +/- √(b²-4ac)]/2a,

The a, b and c coefficients are based on the general form of the quadratic equation: ax² + bx + c. Hence, a=1, b=-3 and c=-10. Substituting the values:

x = [-(-3) +/- √((-3)²-4(1)(-10))]/2(1)

x = 5, -2

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Step-by-step explanation:

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Katen [24]

Answer:

The answer to your question is FJ = 18

Step-by-step explanation:

Data

FG = 30

FH = 12

HE = 8

JH ║GE

These triangles are similar, so we can use proportions to find the length of FJ.

                            \frac{FJ}{FH} = \frac{FG}{FH + HE}

Substitution

                          \frac{FJ}{12} = \frac{30}{12 + 8}

Simplification

                         \frac{FJ}{12} = \frac{30}{20}

Solve for FJ

                        FJ = 12 \frac{30}{20}

Result

                        FJ = 18

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