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3 years ago

Find the sum of arithmetic sequences 4+8+12+16+...+400

Mathematics

2 answers:

Anit [1.1K]3 years ago

7 0

Answer:

20200

Step-by-step explanation:

a=1 × 4=4

a=2 × 4=8

a=3 × 4=12

a = 4 × 4 = 16

400 = 4 + ( n - 1 ) 4]

400 = 4 + 4n - 4

4n = 400

400 / 4n

n = 100

100 / 2 [ 4 + 400 ]

50 [ 404 ]

50 × 404

= 20200

Hope this answer helps you :)

Have a great day

Mark brainliest

mojhsa [17]3 years ago

4 0

Answer:

Step-by-step explanation:

First term = a =4

Common difference = d = 2nd term - first term

d = 8 - 4 = 4

Last term = l = 400

First we have to fin the number of terms 'n'

l = a + (n-1)d

4 + (n-1)*4 = 400

4 + 4n- 4 = 400

4n = 400 {Divide both sides by 4}

n = 400/4

n = 100

$S_{n}=\frac{n}{2}(a + l)\\\\ = \frac{100}{2}*(4+400)\\\\=50 * 404\\\\= 20200$

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Step-by-step explanation:

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3 years ago

Factor: a) 4x^2-13x+9

Fittoniya [83]

Answer:

A. $x = \frac{9}{4}$

B. $x = 1$

Step-by-step explanation:

I don't know if you know this method. I'll explain.

1. Rewrite the same expression, but multiplied and divided by the same number that has the squared variable.

$4(\frac{4x^2-13x+9}{4})$

2. Take this expression to the expression $x^{2} +bx+c$ , you can do this by grouping. (4)( $4x^{2}$ ) can be grouped as $(4x)^2$ ; since what we want is to keep the (4x) in parenthesis, we don't multiply by 13. leaving it like 13(4x). Finally, we multiply 4 * 9 = 36. The denominator remains. Leaving the expression like:

$\frac{(4x)^2-13(4x)+36}{4}$

So you see, we now have the expression $x^2+bx+c$

$x^{2} =(4x)^{2}$

$bx = -13(4x)$

$c = 36$

3. Solve the expression by making 2 parenthesis, extracting (4x) and putting it into both of them like so.

(4x) (4x)

The sign in the first parenthesis is going to be the same as the second number; in this case, negative.

(4x -) (4x)

The sign in the second parenthesis is going to be the multiplication of the second and third signs in front of the numbers. In this case (-) (+) = -

(4x -) (4x -)

Next, we have to find a number that multiplied by another number be equal to ''c'' and added up or substracted (depending on the signs) be equal to ''b''. In this case, since we have the same signs in both parenthesis, we must only find a number which multiplied by another number be equal to 36 and substracted by that number be equal to 13. These two numbers are: 9 and 4 because 9 * 4 = 36 and - 9 + (-4) = -13

Remember that everything is being divided by 4 in this problem.

$\frac{(4x-9)(4x-4)}{4}$

4. Factor. If you have done everything correctly, the factor number will be the same as the one in the denominator. In this case, it's 4.

$(4x-4)$ is factorable. Their common factor number is 4. If you do not remember how to factor, it's basically dividing by a common number or variable.