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3 years ago

Which sequence is arithmetic?

Mathematics

1 answer:

MissTica3 years ago

3 0

Answer:

11, 14, 17, 20

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Consider 2, 6, 18, 54

6 - 2 = 4, 18 - 6 = 12, 54 - 18 = 36 ← no common difference, not arithmetic

Consider 3, 6, 12, 24

6 - 3 = 3, 12 - 6 = 6, 24 - 12 = 12 ← no common difference, not arithmetic

Consider 11, 14, 17, 20

14 - 11 = 3, 17 - 14 = 3, 20 - 17 = 3 ← common difference of 3, so arithmetic

Consider 7, 11, 13, 18

11 - 7 = 4, 13 - 11 = 2, 18 - 13 = 5 ← no common difference, not arithmetic

The arithmetic sequence is 11, 14, 17, 20

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3 years ago

1)A System of equations is shown below . What is the solution to the system of equations? 5x+2y=-15 2x-2y=-6

meriva

Answer:

x= -3 and y= 0

Step-by-step explanation:

5x+2y=-15

2x-2y=-6

7x =-21

x= -3

Putting value of x in equation 1

5(-3) +2y=-15

-15+2y= -15

2y= 0

y= 0

This can be solved with the help of matrices

In matrix form the above equations can be written in the form

$\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]$ $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$ = $\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]$

Let

$\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]$ = A $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$ = X and $\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]$ = B

Then AX= B

or X= A⁻¹ B

where A⁻¹= adj A/ ║A║ where mod A≠ 0

adj A= $\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]$

║A║= ( 5*-2- 2*2)= -10-4= -14≠0

X= A⁻¹ B

$\left[\begin{array}{ccc}x\\y\\\end{array}\right]$ =- 1/14 $\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]$ $\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]$

$\left[\begin{array}{ccc}x\\y\\\end{array}\right]$ =- 1/14 $\left[\begin{array}{ccc}-2*-15&+ -2*-6\\-2*-15&+ 5*-6\\\end{array}\right]$