Answer:
108 th term is zero
Step-by-step explanation:
The nth term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 99 and a₉₉ = 9 then
a₁ + 8d = 99 → (1)
a₁ + 98d = 9 → (2)
Subtract (1) from (2) term by term to eliminate a₁
0 + 90d = - 90
90d = - 90 ( divide both sides by 90 )
d = - 1
Substitute d = - 1 into (1) for value of a₁
a₁ + 8(- 1) = 99
a₁ - 8 = 99 ( add 8 to both sides )
a₁ = 107
Then
107 - (n - 1) = 0
107 - n + 1 = 0
- n + 108 = 0 ( subtract 108 from both sides )
- n = - 108 ( multiply both sides by - 1 )
n = 108
The 108th term is zero
Answer:
3/35
Step-by-step explanation:
Hello from MrBillDoesMath!
The first choice (y = 2x) is NOT the blue line because it has twice of the slope of the line y=x. That is, for a given positive x value the graph of y= 2x appears above the black line which is not the case for the blue line shown.
The second choice (y =.001x) is a possibility but the multiplier .001 is so small I think the graph of that line would be "close" to the x-axis. I don't think it's the blue line.
y = -x. Now here we can say NO! That line goes through the origin all right but has a slope of -1 so is heading "downward" from left to right. That is not the blue line either.
Well, then, it seems that the last equation ( y = 1/2x) is the only remaining reasonable answer.
Regards, MrB.
