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)
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-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:
In order to find the fraction of the 20 dollars that has been spent, we have to divide the amount spent by the total amount. So 0.65 is the fraction of 20 that is spent.
Step-by-step explanation:
Answer:
Given the sequence 20, 24, 28, 32, 36, . . . find the 60th term.
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nth term pattern: a(n) = 20 + (n-1)4
60th term: a(60) = 20 + 59*4 = 256
Step-by-step explanation:
Answer: y=4/3x-2
Y-Intercept: -2
Slope: 4/3
Step-by-step explanation:
On the Y-Axis put -2 because thats the Y-intercept.
And for slope graph a slope of 4/3
Answer: 3x-5
Step-by-step explanation:
Five subtracted from three times any number can be represented as 3x-5.
