Need help with a math question
2 answers:
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Firstly, we will draw diagram of the scenario
Dana reflects point A(2,5) across line small script letter lℓ to get image point Upper A primeA′(6,1)
It means that AA' is perpendicular bisects of line(l)
so, let's assume it intersects at point M
so, M will be mid-point between A and A'
M is a point on line (l)
now, we will find slope of line on AA'
x1=2 , y1=5
x2=6 , y2=1
now, we can plug values
now, we know that line (l) and AA' are perpendicular to each other
so, slope of line(l) is -1/m
slope=1
so, we have slope and a point
now, we can use point slope form of line
now, we can plug values
so, the equation of line (l) is
..............Answer
In 1-4, to determine whether a sequence is either arithmetic or geometric, you need to look at differences of consecutive terms (arithmetic) and ratios of consecutive terms (geometric). If you can't find it, the sequence will fall under the "neither" category.
For example, the differences between consecutive terms in the first sequence are
If the sequence was arithmetic, the difference between consecutive terms would have been the same constant throughout this list. But that's not the case, so this sequence is not arithmetic.
The ratios between consecutive terms are
The sequence would have been geometric if the list contained the same value throughout, but it doesn't. So this sequence is neither arithmetic nor geometric.
Meanwhile, in the second sequence, the differences are
so this sequence is arithmetic.
In 5-6, you know the sequences are arithmetic, so you know that they follow the recursive rule
For example, in the fifth sequence we know the first term is . The common difference between terms is
. So using the rule above, we have the pattern
and so on, so that the -th term is determined entirely by
with the formula
This means the 21st term in the fifth sequence is
The process is simple: identify and
, plug them into the formula above, then evaluate it at whatever
you need to use.