2 + 3y + 9z = 4<br> - x + 8y - 6z = 4<br> x + 3y +3z = 10

A. [4 marks]

storchak [24]

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is $u_{n}=u_{1}+(n-1)d$ , where

$u_{1}$ is the first term
d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is $u_{n}=u_{1}r^{n-1}$ , where

$u_{1}$ is the first term
r is the common ratio between each two consecutive terms $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∵ $u_{1}$ of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ $u_{2}$ , $u_{3}$ , $u_{6}$ are the first 3 terms of a geometric sequence

∵ $u_{2}$ = 1 + (2 - 1)d

∴ $u_{2}$ = 1 + d

∵ $u_{3}$ = 1 + (3 - 1)d

∴ $u_{2}$ = 1 + 2d

∵ $u_{6}$ = 1 + (6 - 1)d

∴ $u_{2}$ = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

(1 + 5d)

∵ The common ratio in the geometric sequence is $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∴ $r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

- Use cross multiplication with the equal fractions

∵ $\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

7 0

3 years ago

How to find only f on a graph that defines a function

puteri [66]

Answer:

Read Below

Step-by-step explanation:

we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.

The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular

x

value. The

y

value of a point where a vertical line intersects a graph represents an output for that input

x

value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that

x

value has more than one output. A function has only one output value for each input value.

3 0

3 years ago

2 x - 17 = 11.<br> Help please

Svet_ta [14]

Step-by-step explanation:

Perhaps you want to solve the equation for the value of x. If so then let us work it out:

$2x - 17 = 11 \\ 2x = 11 + 17 \\ 2x = 28 \\ x = \frac{28}{2} \\ \huge \red { \boxed{x = 14}}$

8 0

3 years ago

Solve for w: v = 3p (w -r)

notka56 [123]

Answer:

Step-by-step explanation:

v=3p(w-r)

v=3pw-3pr

v+3pr=3pw

(v+3pr)/3p=w

7 0

3 years ago

.006 + .0002 in scientific notation

Vilka [71]

6.2 x 10^-3 Because when you add them together you get .0062 so you don't want anymore than one number to the left of decimal when in scientific notation therefore its 6.2 so you wanna move the decimal three spaces to the left to get .0062 therefore its 6.2x10^-3

6 0

3 years ago

2 + 3y + 9z = 4 - x + 8y - 6z = 4 x + 3y +3z = 10