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3 years ago

Find the next four terms in the arithmetic sequence.

Mathematics

2 answers:

kipiarov [429]3 years ago

7 0

Answer:

C: a+6, a+10, a+14, a+18

Step-by-step explanation:

a - 6, a - 2, a + 2, ...

Given is arithmetic sequence

General form of arithmetic sequence is

a , a+d, a+2d , a+3d , a+4d..............

To get next terms we need to find out 'd'

common difference is 'd'

to find 'd' we subtract first term from second term

a -2 - (a-6)= a-2 -a +6 = +4

d= 4

So we add 4 to get next four terms

a+ 2 is the last term

a+2 +4 = a+6

a+6 + 4= a+10

a+ 10 + 4= a+14

a+14 + 4= a+18

so next four terms are

a+6, a+10, a+14, a+18

frutty [35]3 years ago

5 0

C because they are just adding 4 each time.

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vredina [299]

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4 years ago

Simplify; 1/x^2+5x+6 + 1/x^2+3x+2 pls I need a step by step solution urgently

ikadub [295]

Answer:

The simplest form of $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$ is $\frac{2}{(x+1)(x+3)}$

Step-by-step explanation:

To add two algebraic fractions do these steps

Factorize each denominator
Simplify each fraction to its lowest term
Find the LCM of the two denominators
Divide LCM by each denominator and multiply the numerators by its corresponding quotients
Add the two fraction and simplify the last answer

To simplify $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$

Factorize each denominator

∵ The denominator of the first fraction is x² + 5x + 6

∵ x² = (x)(x)

∵ 6 = (2)(3)

∵ (2)(x) + (3)(x) = 5x ⇒ middle term

∴ x² + 5x + 6 = (x + 2)(x + 3)

∵ The denominator of the second fraction is x² + 3x + 2

∵ x² = (x)(x)

∵ 2 = (2)(1)

∵ (2)(x) + (1)(x) = 3x ⇒ middle term

∴ x² + 3x + 2 = (x + 2)(x + 1)

Find the LCM of the two denominators

∵ The denominators are (x + 2)(x + 3) and (x + 2)(x + 1)

- LCM is all the different factors multiplied together

∴ LCM of them is (x + 1)(x + 2)(x + 3)

- Divide LCM by each denominator

∵ (x + 1)(x + 2)(x + 3) ÷ (x + 2)(x + 3) = (x + 1)

- Multiply the numerator of the first fraction by (x + 1)

∵ (x + 1)(x + 2)(x + 3) ÷ (x + 2)(x + 1) = (x + 3)

- Multiply the numerator of the second fraction by (x + 3)

∴ $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$ = $\frac{x+1}{(x+1)(x+2)(x+3)}+\frac{x+3}{(x+1)(x+2)(x+3)}$

- Add the numerators and write the answer as a single fraction

∴ $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$ = $\frac{2x+4}{(x+1)(x+2)(x+3)}$

- Factorize the numerator by taking 2 as a common factor

∵ 2x + 4 = 2(x + 2)

∴ $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$ = $\frac{2(x+2)}{(x+1)(x+2)(x+3)}$

- Simplify the fraction by dividing up and down by (x + 2)

∴ $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$ = $\frac{2}{(x+1)(x+3)}$

The simplest form of $\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}$ is $\frac{2}{(x+1)(x+3)}$

5 0

4 years ago

LOOK AT THE PICTURE PLEASE ANSWER FAST

AlladinOne [14]

The answer is B. Would you like an explanation why?

7 0

3 years ago

3s+6≤-5(s+2)

dybincka [34]

Your answer for the first inequality is D) s less than or equal to -2

2nd inequality: I got the answer s<55/8.

3 0

3 years ago

A calculator that cost $60 in 1980 now sells for $10. What was the percent of decrease

Romashka-Z-Leto [24]

Answer: 16.6%

Step-by-step explanation:

$60 divided by 6 = $10

so divide 100 by 6 and you get about 16.6

I Hope this Helps!

4 0

3 years ago

Read 2 more answers