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
-2/3 is the simplified form of the expression -1/2 ÷ 3/4.
<h3>What is the simplified form of the given expression?</h3>
Given the expression in the question;
-1/2 ÷ 3/4
To divide by a fraction, multiply by its reciprocal.
-1/2 ÷ 3/4
Reciprocal of 3/4 is 4/3
Hence
-1/2 × 4/3
Next, we cancel out the common factor of 2
Factor out 2 from 4
-1/2 × 2(2)/3
-1/1 × 2/3
( -1 × 2 ) / ( 1 × 3 )
(-2) / (3)
-2/3
Therefore, the simplified form is -2/3
Learn how to solve more fraction problems here: brainly.com/question/1627825
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<span>Y=-4x-7 in standard form is,</span> y + 4 * x + 7 = 0
Answer:
x=1
Step-by-step explanation:
it is the point of intersection of both lines which (1,1)
for x=1 both produce same value i.e.,1
