MATHEMATICS HIGH SCHOOL

8The first term of an arithmetic sequence is 5. The third term of the sequence is 13.
Which of the following expressions represents the nth term of the sequence?
A 4n +1
B) 4n + 5
5n+1
D) 5n + 5

Answers

Answer 1
Answer:

If the first term of an arithmetic sequence is 5 and the third term of the sequence is 13 then the nth term is A) 4n +1.

What are arithmetic and geometric sequence?

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference(d).

aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, The first term of an arithmetic sequence is 5.

The third term of the sequence is 13.

As we can conclude that for 2 terms the common difference is increased by 8.

∴ Common difference (d) = 8/2 = 4.

Now, we know the nth term of an arithmetic sequence is,

aₙ = a₁ + (n - 1).d.

aₙ = 5 + (n - 1)×4.

aₙ = 5 + 4n - 4.

aₙ = 4n + 1.

learn more about arithmetic sequence here :

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Answer 2
Answer:

Answer:A 4n+1

Step-by-step explanation: found the answer key

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Solve to three significant digits 123= 500e ^ -0.12x

Answers

500{ e }^( -0.12x )=123\n \n { e }^{ -\frac { 12 }{ 100 } x }=\frac { 123 }{ 500 } \n \n { e }^{ -\frac { 3 }{ 25 } x }=\frac { 123 }{ 500 }

\n \n { \left( { e }^( x ) \right) }^{ -\frac { 3 }{ 25 } }=\frac { 123 }{ 500 } \n \n { e }^( x )={ \left( \frac { 123 }{ 500 } \right) }^{ \frac { 1 }{ -\frac { 3 }{ 25 } } }

\n \n { e }^( x )={ \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } }\n \n \ln { \left( { \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } } \right) } =x

\n \n x=-\frac { 25 }{ 3 } \ln { \left( \frac { 123 }{ 500 } \right) }

\therefore \quad x\approx 11.7

Williams salary is £24000 his salary increases by 4% work out Williams new salary

Answers

100%  = 24000 
50 %  =  12000
10%   =   2400
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1 %    = 240

Given h(x) = x24, find h(-8)

Answers

Answer:

-192

Step-by-step explanation:

replace the x with -8 and multiply

Why might a person need an emergency plan?

Answers

that way they have something to fall back on just in case of an emergency.

For a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 7.38 centimeters? (Use the value of 3.14 to represent pi, and the formula for circumference = 2*pi*r)

Answers

A button with a circumference of 7.38 cm will need a buttonhole with the size of 2.35 cm.

Since the circumference is equivalent to 7.38 cm, the formula can be displayed as follows:
7.38 cm = 2πr
r = 7.38cm/2π
r= 1.1751592 cm
diameter = 2r
               = 2.3503184 cm or approximately 2.35 cm

Please help me on this

Answers

Answer: Choice C

Converse of the corresponding angles postulate

============================================

Explanation:

The corresponding angles postulate says that if we have two parallel lines, then the corresponding angles are congruent.

The converse of this is where we go in reverse: if we know the corresponding angles are congruent, then the lines are parallel.

Corresponding angles are ones where they are on the same side of the transversal line, and also on the same side of each adjacent parallel line. In this case, the angles 52 are to the right of the tranversal, and each are above their neighboring parallel line. We could say the two corresponding angles are both in the upper right hand corner (think of the two lines crossing to form 4 corners or regions)
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