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frosja888 [35]
3 years ago
12

The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for th

e nth term of this sequence? 1. an = 8n + 10 2. an = 8n − 14 3. an = 16n + 10 4. an = 16n − 38

Mathematics
2 answers:
Lynna [10]3 years ago
8 0
The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for the nth term of this sequence?
1. an = 8n + 10
☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆ 2. an = 8n − 14
3. an = 16n + 10
4. an = 16n − 38

Ilia_Sergeevich [38]3 years ago
6 0

Answer:

Option 2nd is correct

a_n =8n-14

Step-by-step explanation:

The nth term for the arithmetic equation is give by:

a_n = a_1+(n-1)d             ....[A]

where,

a_1 is the first term

d is the common difference and

n is the number of term.

As per the statement:

The fourth term in an arithmetic sequence is 18 and the seventh term is 42

⇒a_4 = 18 and a_7 = 42

then by above definition we have;

a_1+3d = 18             .....[1]

a_1+6d = 42            .....[2]

Subtract equation [1] from [2] we have;

3d = 24

Divide both sides by 3 we have;

d = 8

Substitute in [1] we have;

a_1+24 = 18

Subtract 24 from both sides we have;

a_1=-6

We have to find the equation for the nth term of this sequence

Substitute the given values in [A] we have;

a_n = -6+(n-1)\cdot 8

⇒a_n = -6+8n-8

⇒a_n =8n-14

Therefore, an equation for the nth term of this sequence is, a_n =8n-14

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Answer:

Option C -M'K' is the same length as MK

Step-by-step explanation:

Given : Line segment MK has endpoints at (2, 3) and (5,4)

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By definition of reflection: reflection of point (x,y) across the the y-axis is the point (-x,y)

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⇒d=\sqrt{9+1}

⇒d=\sqrt{10}   ....(1)

Now, we find the length of M'K'

let (x_1^{'},y_1^{'})=(-2,3)\\\\(x_2^{'},y_2^{'})=(-5,4)

d^{'}=\sqrt{(x_2^{'}-x_1^{'})^2+(y_2^{'}-y_1^{'})^2}

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from (1) and (2) we simply show that the length of MK and M'K' is equal

we can also refer the figure attached for reflection of MK and M'K'

therefore, Option C is correct


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