What arithmetic sequence with a_{4}=18 and a_{10}=48
1 answer:
Answer:
= 5n - 2
Step-by-step explanation:
the nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₄ = 18 and a₁₀ = 48 , then
a₁ + 3d = 18 → (1)
a₁ + 9d = 48 → (2)
subtract (1) from (2) term by term to eliminate a₁
6d = 30 ( divide both sides by 6 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 18
a₁ + 15 = 18 ( subtract 15 from both sides )
a₁ = 3
Then
= 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2
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Answer:
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula:
Given points: (-6, 4), (6, 10)
(-6, 4) = (x1, y1)
(6, 10) = (x2, y2)
To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.
First, let's find the slope. To do this, input the given points into the slope formula:
Simplify:
10 - 4 = 6
6 - (-6) = 6 + 6 = 12
The slope is .
To find the y-intercept, input the slope and one of the given points(in this example I'll use point (6, 10)) into the equation and solve for b:
10 = 3 + b
7 = b
The y-intercept is 7.
Now that we know the slope and the y-intercept, we can write the equation: