Can someone help me solve this?
1 answer:
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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
The equation of the line from give points is y = 2/3x - 5/3.
According to the statement
We have given that the two points which are (-2,-3) and (4,1)
And we have to find the equation of a line that passes through the given points.
So,For this purpose,
First, we need to determine the slope of the line. The slope can be found by using the formula:
Where
m is the slope and
Substituting the values from the points in the problem gives:
m = 1 + 3 /4 + 2
m = 4/6
m = 2/3.
And then
Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:
Put the values in it then
y - (-3) = 2/3 (x-(-2))
y +3 = 2/3 (x +2)
3y + 9 = 2x + 4
3y - 2x = 4 -9
3y -2x = -5
3y = 2x - 5
y = 2/3x - 5/3.
So, The equation of the line from give points is y = 2/3x - 5/3.
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