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n200080 [17]
3 years ago
9

Find the fifth term in the sequence

Mathematics
1 answer:
kvv77 [185]3 years ago
8 0

Method 1:

The recursive formula states that every next term is three times the previous one, plus two.

So, we have:

  • a_1 = 1
  • a_2 = 3\cdot 1 + 2 = 3+2 = 5
  • a_3 = 3\cdot 5 + 2 = 15+2 = 17
  • a_4 = 3\cdot 17 +2 = 51+2 = 53
  • a_5 = 3\cdot 53 +2 = 159+2 = 161

Method 2:

You can write the expression for a_5, and use the recursive formula until you get to the starting point:

a_5 = 3a_4+2 = 3(3a_3+2)+2 = 9a_3+8 = 9(3a_2+2)+8 = 27a_2+26 = 27(3a_1+2)+26 = 81a_1+80

Now use the fact that a_1 = 1 to get the conclusion

a_5 = 81+80 = 161

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The sum of x and it’s opposite is always zero?
jeka94

Answer:

1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies

2) Now let's consider any real number a no matter positive or negative we will have that:

a-a =0

Or in the other case:

-a -(-a) =-a +a=0

So then we can conclude that the expression is a general rule and is true

Step-by-step explanation:

For this case we can verify if the following expression is true or false:

The sum of x and it’s opposite is always zero?

If we want to proof this we need to show that for any number is true.

1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies

2) Now let's consider any real number a no matter positive or negative we will have that:

a-a =0

Or in the other case:

-a -(-a) =-a +a=0

So then we can conclude that the expression is a general rule and is true

5 0
3 years ago
1. Determine the measure of the unknown angles indicated by letters. Justify your answers with
Maurinko [17]

Answer:

hello,

Step-by-step explanation:

a)

In an isocele triangle, base's angles have the measure:

42+2a=180

2a=180-42

a=69(°)

b)

in a triangle, an external angle has for measure the sum of the angles not adjacents.

55+b=132

b=77 (°)

c)

in a quadrilater the sum of the (interior) angles is 2*180=360 degrees.

90+90+68+c=360

c=360-90-90-68

c=112 (°)

7 0
2 years ago
Vernon's work for finding the value of x is shown below. Lines A C and B D intersect at point E. Angle A E D is (16 x + 8) degre
Marta_Voda [28]

Answer:

<em>No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other</em>

Step-by-step explanation:

Find the diagram attached

If line AC and BD intersects, then m<AED + m<DEC = 180 (sum of angle on a straight line is 180 degrees)

Given

m<AED = 16x+8

m<DEC = 76 degrees

16x + 8 + 76 = 180

16x + 84 = 180

16x = 180-84

16x = 96

x = 96/16

x = 6

Hence the value of x is 6

Hence the correct option is <em>No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other</em>

5 0
2 years ago
Read 2 more answers
A firm has a beta of 1.3 and a debt-to-equity ratio of .4. The market rate of return is 11.6
Citrus2011 [14]

Beta= 1.3

Debt to equity ratio= 0.4

Market rate of return= 11.6%

= 11.6/100

= 0.116

Tax rate= 32%

= 32/100

= 0.32

Risk free rate=  3.3%

= 3.3/100

= 0.033

Pretax cost of debt= 7.2%

= 7.2/100

= 0.072

The firm's WACC can be calacluated as follows

RS= 0.033+1.3(0.116-0.033)

= 0.033+1.3(0.083)

= 0.033+0.1079

= 0.1409

WACC= (1/1.4)(0.1409)+(2/1.4) (0.072)(1-0.32)

= (0.7142)(0.1409) + (1.4285)(0.072)(0.68)

= 0.1006+0.0699

= 0.1705(100)

= 17.05%

Hence the firm's WACC is 17.05%

6 0
2 years ago
a school principal orders 75 boxes of chalk. each box has 12 sticks of chalk, the school has 23 teachers. Does the principal hav
Zolol [24]
Well 75x12=900 so 900 divided by 40 is 22.5 so 22 teachers can have 40 chalks but the principal needs to order another 20 :)
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