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
Answer:
105 and 106
Step-by-step explanation:
The consecutive pages are such that the difference between the numbers of these pages is 1. As such, if the number on the first of the two pages is x, the second will be x + 1.
Hence, given that the sum of the numbers two pages is 211,
x + x + 1 = 211
2x = 210
x = 105, the next
= 105 + 1
= 106
3x + 5y = 11
5y = -3x + 11
y = -3/5x + 11/5.....slope here is -3/5. A parallel line will have the same slope.
y = mx + b
slope(m) = -3/5
(15,4)...x = 15 and y = 4
now we sub and find b, the y int
4 = 15(-3/5) + b
4 = - 9 + b
4 + 9 = b
13 = b
ur equation is : y = -3/5x + 13
270+26x is less than or equal to 1325
26x is less than or equal to 1055
x is less than or equal to 40
