1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
user100 [1]
3 years ago
8

In an arithmetic sequence, t4 + t5 + t6 = 300, and t15 +t16+ t17 = 201. Find t18.

Mathematics
1 answer:
stiks02 [169]3 years ago
5 0
In an arithmetic sequence:
Tn=t₁+(n-1)d

t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d

t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d

Therefore:
3t₁+12d=300    (1)


t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d

t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d

Therefore:
3t₁+45d=201    (2)

With the equations (1) and (2) we make an system of equations:

3t₁+12d=300
3t₁+45d=201

we can solve this system of equations by reduction method.

  3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
       -33d=99      ⇒d=99/-33=-3

3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112

Threfore:

Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n

Now, we calculate T₁₈:

T₁₈=115-3(18)=115-54=61

Answer: T₁₈=61




You might be interested in
dawn has 5/6 yard of lace. She uses 4/5 of it for a dress and the rest for a jewel box. How much lace does she use for the jewel
GrogVix [38]
amount\ used\ for\ jewel\ box=all\ lace-\ lace\ used\ for\ dress\\\\\
amount\ used\ for\ jewel\ box=\frac{5}{6}-\frac{4}{5}=\frac{25}{30}-\frac{24}{30}=\frac{1}{30}\\\\ \frac{1}{30}\ of\ lace\ is\ for\ jewel\ box.

3 0
3 years ago
Read 2 more answers
write an equation in point-point form for the line through the given point with the givedescribe how the graph of y | x| -4 is l
Digiron [165]
a) The point-slope form of the equation of a line through point (h, k) with slope m is
  y - k = m(x - h)

In point-slope form, the equation of the line through (-3, -7) with slope -6/5 is
  y + 7 = (-6/5)(x + 3)


b) The graph of
  y = |x|-4
represents a translation downward 4 units of the graph of
  y = |x|
It retains the same general shape and axis of symmetry, but will have two (2) x-intercepts instead of one (1).

4 0
3 years ago
Suppose you have a die that has 20 sides numbered 1 to 20. What is the probability the
Digiron [165]

Answer:

\frac{1}{10}

Step-by-step explanation:

3 0
3 years ago
A company that makes hair-care products had 2,000 people try a new shampoo. Of the 2,000 people, 4 had a mild allergic reaction.
bazaltina [42]

Answer:

0.2%

Step-by-step explanation:

2,000 people tested the new shampoo.

4 people had a mild allergic reaction.

4 is what percentage of 2,000?

0.2 percent.

(2,000 = %99.8)

4 0
2 years ago
Karen has 4h storyboiks. Karen's storybook collection is 2/3 of what Mary's collection is. How many storybooks do they have in a
Dafna11 [192]
In order to find out the answer , you just need to count :
Let's say that mary's collection is symbolized by x

2/3  x     =   4h

x             = 3/2 . 4h

x           =    6h

The storybooks they have in total would be : 6h  + 4h = 10 h

hope this helps

6 0
3 years ago
Other questions:
  • X squared +x (×-5)-×+7
    8·2 answers
  • A running track in the shape of an oval is shown. The ends of the track form semicircles.What is the perimeter of the inside of
    6·2 answers
  • Can any one slove this
    13·1 answer
  • Solve y^3 =-28 where y is a real number.<br> Simplify your answer as much as possible.
    9·2 answers
  • Help! due in 5 mins
    11·1 answer
  • Scott's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make copper balls tha
    11·1 answer
  • The area of a regular hexagon inscribed in a circle with radius 5 is what . Round your answer to the nearest whole number.
    12·1 answer
  • Would y=x be proportional or nonproportional?​
    14·2 answers
  • Perform the indicated operation.<br> (8-15i)+(-3+2i)
    5·2 answers
  • Suppose f(x) = x^2 - 8<br> Evaluate f(2) - f(-3)
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!