Please help, (AP is arithemtic progression)
1 answer:
Answer:
p = 8
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 4 + 5p and d = 5, then
a₁ + 8d = 4 + 5p, that is
a₁ + 8(5) = 4 + 5p
a₁ + 40 = 4 + 5p ( subtract 40 from both sides )
a₁ = 5p - 36
a₂ = 5p - 36 + 5 = 5p - 31
a₃ = 5p - 31 + 5 = 5p - 26
a₄ = 5p - 26 + 5 = 5p - 21
Given that the sum of the first 4 terms = 7p - 10, then
5p - 36 + 5p - 31 + 5p - 26 + 5p - 21 = 7p - 10, that is
20p - 114 = 7p - 10 ( subtract 7p from both sides )
13p - 114 = - 10 ( add 114 to both sides )
13p = 104 ( divide both sides by 13 )
p = 8
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Slope intercept form of a line perpendicular to 3x + y = -8, and passing through (-3,1) is
<u>Solution:</u>
Need to write equation of line perpendicular to 3x+y = -8 and passes through the point (-3,1).
Generic slope intercept form of a line is given by y = mx + c
where m = slope of the line.
Let's first find slope intercept form of 3x + y = -8
3x + y = -8
=> y = -3x - 8
On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c , we can say that for line 3x + y = -8 , slope m = -3
And as the line passing through (-3,1) and is perpendicular to 3x + y = -8, product of slopes of two line will be -1 as lies are perpendicular.
Let required slope = x
So we need to find the equation of a line whose slope is and passing through (-3,1)
Equation of line passing through and having lope of m is given by
Substituting the values we get,
Hence the required equation of line is found using slope intercept form