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:
volume of cone = 12.56 cubic units
Step-by-step explanation:
Volume of cone = 1/3 π r² h
r = 2
h = 3
then
V= 1/3 3.14 * (2) ² 3
= 12.56 cubic units
It would be .75x=25-13
So .75x=12
x=16 because .75×16=12
Answer:
1 and 2 are correct!! Good Job!!
3. on the number line put a solid dot over 0, the line should to the right.
4. on the number line put a solid dot over -4, the line will go to the left.
5. on the number line put a open dot over 1.5, the line will go to the left.
Step-by-step explanation:
I hope this helps!! Also, you did great on 1 and 2, got this!!
