if -8,m,n,19 are arithmetic progression, find(m,n).
to be in AP,
n-m = m - (-8) and 19-n = n-m
n - m = m + 8 ----> n = 2m + 8 **
and
m = 2n - 19 ***
sub *** into **
n = 2(2n-19) + 8
n = 4n - 30
n= 10
then in ***, m = 1
(m,n) = (1,10)
check: are -8 , 1 , 10, and 19 in AP ? Yes, they have a common
difference of 9
Ms. Sue is right in her computation. But can you use her answer to figure what comes next? She has figured out that the common difference is 9, since 19 is three terms after -8. Now you can use that to find m and n.
Or, since there is a common difference, you know that
(m+8) = n-m
n-m = 19-n
Now just find m and n.
Well, I can certainly help you find a good laugh, but finding (m, n) might be a bit trickier. Do you happen to have any other details or clues about (m, n)? Maybe a hint or a funny joke to share?
To find the values of m and n in the arithmetic progression -8, m, n, 19, we need to use the formula for an arithmetic progression.
An arithmetic progression is a sequence in which the difference between each term and the previous term is constant.
First, let's find the common difference (d) between consecutive terms. The common difference is given by:
d = (n - m) / 2
Since the common difference is constant, it should be the same as the difference between any two consecutive terms in the sequence. In this case, we can take the difference between the second and first terms, or the difference between the fourth and third terms:
-8 - m = m - n
n - m = 19 - n
Combining these two equations, we have:
-8 - m = 19 - n
m - n = n - m
Now, we can solve these equations simultaneously to find the values of m and n.
Rearranging the first equation, we get:
m + n = -8 + 19
m + n = 11
Rearranging the second equation, we get:
2m = 2n
m = n
Now, we can substitute m = n in the equation m + n = 11:
2m = 11
m = 11/2
Therefore, the values of m and n in the arithmetic progression -8, m, n, 19 are m = 11/2 and n = 11/2.