Answer:
an = 3n - 3
Step-by-step explanation:
The nth term of an arithmetic progression is expressed as;
an = a + (n-1)d
a is the first term
n is the number of terms
d is the common difference
a8 = a + (8-1)d
a8 = a + 7d = 21 ....1
a10 = a+9d = 27 ....2
Subtract 1 from 2
7d - 9d = 21 - 27
-2d = -6
d = -6/-2
d = 3
Since a + 7d = 21
a + 7(3) = 31
a + 21 = 21
a = 21 - 21
a = 0
Get the nth term
Recall that an = a + (n-1)d
an = 0 + (n-1)*3
an = 3n - 3
Hence the nth term of the sequence is 3n - 3
Answer:
67.9705...
Add the two numbers.
67 16/34 + 14/28 = 67.9605...
That is your answer.
Answer:
Step-by-step explanation:
B + 87 +78 +66 = 360
B = 129 °
the angle next to B then is
180 = 129 + b '
51 ° = b '
A + 61 + b ' = 180
A = 68 °
Answer:
Step-by-step explanation:
The equation of the line you will find should be in the form y =mx+c , where m is the gradient and c is the y intercept.
The gradient of a line that is perpendicular to a line [of a known gradient] is the negative reciprocal of the gradient of the first. i.e. if a is the known gradient and the perpendicular gradient is b, ab = -1. Therefore the -3b=-1 and b= 1/3
you can now write y = mx +c as y = 1/3x +c
As you have been given a coordinate, you can input these values into y= 1/3x + c
-12 = 1/3(6) +c
-12 - 2 = c
c = -14
hence the equation of the line is y= 1/3x -14
Answer:
a) there is s such that <u>r>s</u> and s is <u>positive</u>
b) For any <u>r>0</u> , <u>there exists s>0</u> such that s<r
Step-by-step explanation:
a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.
b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.
