What is a1 of the arithmetic sequence for which a3=10 and a51=−182?
1 answer:
Answer:
a₁ = 18
Step-by-step explanation:
The n th term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 10 and a₅₁ = - 182, then
a₁ + 2d = 10 → (1)
a₁ + 50d = - 182 → (2)
Subtract (1) from (2) term by term to eliminate a₁
48d = - 192 ( divide both sides by 48 )
d = - 4
Substitute d = - 4 into (1) and evaluate for a₁
a₁ + 2(- 4) = 10
a₁ - 8 = 10 ( add 8 to both sides )
a₁ = 18
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Answer:
y=-3x+7
Step-by-step explanation:
y=mx+b is the formula you are going to end up once completed.
This, by given two points:
(4,-5) (3,-2)
= Point-Slope Intercept Form
= After subtracting both from above
-3 = is your slope, decreasing.
Substitute -3 for y=mx+b
y=-3x+b
Use one of the given points (any) to find what b equals.
(4,-5)
x y
-5=-3(4)+b
-5= -12+b
7=b
Final Equation:
y=-3x+7