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34kurt
3 years ago
8

What is the fifth term of the geometric sequence whose first three terms are 486, 162, and 54?

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0

Answer:

6

Step-by-step explanation:

an = ar^(n-1)

a = first term

n = nth term

r = common ratio

r = r2 / r1 = r3 / r2

The first 3 terms are :

486, 162, and 54

Hence,

a = 486

r = 162 / 486 = 1/3

Hence ;

a5 = 486(1/3)^5 - 1

a5 = 486(1/3)^4

a5 = 486(1 / 81)

a5 = 486 * 1 / 81

a5 = 486 / 81

a5 = 6

The 5th term of the geometric progression will be ; 6

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Find m∠STU and m∠TUA
PIT_PIT [208]

Answers:

  • angle STU = 65 degrees
  • angle TUA = 123 degrees

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

Explanation:

Let's find the expression for angle TUS in terms of x

Angle TUA has the expression 11x+2. It will add to angle TUS to get 180 degrees

(angle TUS) + (angle TUA) = 180

angle TUS = 180 - (angle TUA)

angle TUS = 180 - (11x + 2)

angle TUS = 180 - 11x - 2

angle TUS = -11x + 178

Now focus on the interior angles of triangle TUS. We have these three angles

  • T = 5x+10
  • U = -11x+178
  • S = 58

For any triangle, the interior angles always add to 180, so,

T+U+S = 180

(5x+10) + (-11x+178) + (58) = 180

(5x-11x) + (10+178+58) = 180

-6x + 246 = 180

-6x = 180-246

-6x = -66

x = -66/(-6)

x = 11

Use this x value to find the angle measures we're after:

  • angle STU = 5x+10 = 5*11+10 = 55+10 = 65 degrees
  • angle TUA = 11x+2 = 11*11+2 = 121+2 = 123 degrees

--------------------------

As an alternative route, you can apply the remote interior angle theorem. This says that adding two interior angles leads to the exterior angle that isn't adjacent to either one.

In this case, we would say

(angle STU) + (angle TSU) = angle TUA

that leads to the equation

(5x+10) + (58) = 11x+2

Solving this should lead to x = 11 to generate the angles mentioned earlier.

6 0
3 years ago
2².23 =<br> (Type your answer using exponential notation. Simplify your answer.)
sveta [45]

Answer:

2^2 * 2^3 = 32

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Step-by-step explanation:

2*2*2*2*2 = 32

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3(7/16) in your calculator should do it
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katovenus [111]
There is no property that can be used but you can find the answer by dividing 72 and 6

4 0
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Read 2 more answers
The figure is congruent to the blue figure.
SOVA2 [1]

Answer:

  see attached

Step-by-step explanation:

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