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3 years ago

Solve the question: (-4)+(-1)+2+5+...+x=437

1 answer:

6 0

The sequence is an arithmetic sequence with
a₁ = -4

d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3

an = x

Sn = 437

General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)

We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7

Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874

Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.

Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50

The solution is 50

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Answer:

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Step-by-step explanation:

step 1

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we know that

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In this problem we have

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substitute in the formula

$V=(\frac{5}{2})(\frac{5}{2})(5)=\frac{125}{4}=31.25\ cm^{3}$

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3 years ago

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Step-by-step explanation:

Let xy = k, where k is the constant of variation.

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2 years ago

Evaluate the expression

larisa86 [58]

Answer:

$12-[20-2(6^2\div3\times2^2)]=88$

Step-by-step explanation:

So we have the expression:

$12-[20-2(6^2\div3\times2^2)]$

Recall the order of operations or PEMDAS:

P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.

E: Within the parentheses, if exponents are present, do them before all other operations.

M/D: Multiplication and division next, whichever comes first.

A/S: Addition and subtraction next, whichever comes first.

(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)

Thus, we should do the operations inside the parentheses first. Therefore:

$12-[20-2(6^2\div3\times2^2)]$

The parentheses is:

$(6^2\div3\times2^2)$