Question

Find the three arithmetic means between 12 and -16.

Answer 1

5, -2, -9

5, -1, -9

6, -2, -9

6, -1, -8

Answer 2

Oh k so do you know the formula for arithmetic means?

Answer 3

no

Answer 4

np let me tell u that one:
\[\huge{\textbf{Arithmetic mean} =\frac{a+b}{2}}\]

where a and b are no.

Answer 5

so we have

arithmetic mean = (12-16)/2 = -4/2 = -2

this is the first AM

Answer 6

if u insert AMs the resulting five nos. will be in an Arithmetic progression
now the first term is given 12 and the 5th term is -16 (as there are 3 AMs apart from 12 and -16)
thus there difference is -16- 12
now the gap between the 1st term and the 5th term is of 4 times th egap between 1st and second (in AP the diffence of terms is constant)
thus the constant diffeernce is -28/4=-7
thus the numbers are (12-7),(12-7-7),(12-7-7-7) i.e.5, -2, -9

Answer 7

for finding another two we have:

-16 = 12 + (28-1)d

-16 = 12+ 27*d
-28 = 27 d

d = -28/27

Answer 8

is it c?

Answer 9

no its a

Answer 10

a)

Answer 11

thank you!

Answer 12

np