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
Answer:
The answer to your question is r = 4 in
Step-by-step explanation:
Data
Volume = 4000 π in³
height = 250 in
radius = ?
Process
1.- Look the formula to calculate the volume of a cylinder
Volume = πr²h
2.- Solve for r²
r² = Volume / πh
3.- Substitution
r² = 4000π / π(250)
4.- Simplification
r² = 16
r = √16
5.- Result
r = 4 in
Answer: 14/3 miles
Step-by-step explanation: Miles divided by hours gives speed
1/3÷1/6 = 2 mph
Distance= speed × time
2 1/3 is 7/3 7/3×2 = 14/3
Answer:
33 = x + (3x + 1)
x = bath bombs
So 3x is three times as many bath bombs, then the plus one makes it so that the soaps sold is more than three times the amount of bath bombs sold
Answer:
See below
Step-by-step explanation:
Julie wants to cut her hair 9 inches off from 16 inches
<h3>Part A </h3>
Expression
<h3>Part B</h3>
Calculation
<h3>Part C</h3>
Explanation of steps
- 1 - note the point 16 on the number line
- 2 - move left by 9 points on the number line
- 3 - note point 7 as answer
