Question

if -8,m,n,19 are arithmetic progression, find(m,n).

Answer 1

(19 + 8) / 3 = ?

Answer 2

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

Answer 3

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.