Ask question

Ask question

All categories

3 years ago

14

The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added t

o get - 30?

1 answer:

Thepotemich [5.8K]3 years ago

4 0

Answer:

20 terms

Step-by-step explanation:

<u>Given AP with the first two terms:</u>

a₁= 27 and a₂=24

<u>Common difference: </u>

d= 24-27 = -3

<u>To find </u>

n for which Sₙ= -30

<h3>Solution</h3>

Sₙ = 1/2*n*(a₁+aₙ) =
1/2n(a₁+a₁+(n-1)d) =
1/2n(27+27+(n-1)(-3))=
1/2n(54 - 3n + 3) =
1/2n(57 - 3n)

<u>Since Sₙ = -30</u>

1/2n(57 - 3n) = -30
57n - 3n² = -60
19n - n²- 20 = 0
n² -19 n -20= 0

<u>Solving the quadratic equation we get:</u>

n =20

So the sum of 20 terms will add up - 30

You might be interested in

A grandmother deposited $4,000 in an account that pays 5% per year compounded annually when her granddaughter was born. What wil

Leya [2.2K]

A = P (1 + r/n)^nt
A = 4000(1 + 0.05/1)^(13)(1)
A = $7542.59

4 0

3 years ago

Which property is shown by 6+9=9+6?

Zepler [3.9K]

I think associative property of addition

4 0

3 years ago

Read 2 more answers

The amount Denise charges to repair computers $50 an hour plus a $25 service fee write an expression to show how much she will c

Natalija [7]

The answer you are looking for is 50h+25
Hope that this helps!

4 0

3 years ago

Read 2 more answers

4.A store pays $85 for a table. The markup is 90%. What is the selling price?

allochka39001 [22]

Answer:

$161.50

Step-by-step explanation:

the revenue for an item of $85 with a 90% markup is $161.50

3 0

3 years ago

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0

3 years ago