Question

how do i find Find two arithmetic means between 67 and 90.

Answer 1

call the two unknowns a and b.
you then have a sequence: 67, a, b, 90

Answer 2

the difference between pair of terms has to be the same

Answer 3

67 m1 m2 90

asaneer got it :)

Answer 4

use that to form a set of equations and solve to find a and b

Answer 5

midpoint is 1 mean between 2 values: (a+b)/2 = common difference

in order to find 2 means, we divide by 3: (a+b)/3 = common difference

in order to find n means, we divide by n+1: (a+b)/(n+1) = common difference

Answer 6

...or something akin to that eh :)

Answer 7

@maine2 do you know how to proceed?

Answer 8

another way of viewing this is to take a standard arithmetic sequence:

a, a+d, a+2d, a+3d, ...

where a is the first term and d is the common difference.

in your case you have 67, m1, m2, 90

so we know a=67
and a+3d=90 which implies 67 + 3d = 90

use that to find d and then you have the full sequence

Answer 9

how do find d

Answer 10

solve this: 67 + 3d = 90

Answer 11

23

Answer 12

please show your steps so that I can spot where you may have made a mistake

Answer 13

i just dif 90-67=23

Answer 14

start with:

67 + 3d = 90

and show each step please

Answer 15

?

Answer 16

67+3d=90
-67 -67
3d=23
divide by 3
d=7.66

Answer 17

correct, although 7.66 is an approximation. I would leave it as a fraction, i.e. \(\displaystyle7\frac{2}{3}\)

Answer 18

now recall that the sequence you had was of the form:

a, a+d, a+2d, a+3d

and you know a=67 and you just calculated d=7 2/3, so now you should be able to find the middle two terms

Answer 19

ok so a+d is 234/3

Answer 20

don't keep it as a mixed fraction, instead work it out as a+d=67 + 7 2/3 = ?

Answer 21

67 + 7 = ?

Answer 22

74

Answer 23

sorry I meant to say "don't keep it as an improper fraction.." up there.

Answer 24

yes, so a+d = 67 + 7 2/3 = 74 2/3

Answer 25

now you need a+2d = (a+d)+d = 74 2/3 + 7 2/3 = ?

Answer 26

so it is 81

Answer 27

74 + 7 = 81 yes
but you also need the fractional part: 2/3 + 2/3 = ?

Answer 28

1.3

Answer 29

:/ yes - but leave as a fraction please, so its 1 1/3

Answer 30

so 3rd term = 81 + 1 1/3 = ?

Answer 31

so it is 82 1/3

Answer 32

yes, so your final sequence is:\[67, 74\frac{2}{3},82\frac{1}{3},90\]

Answer 33

well done! :)

Answer 34

thanks asnaseer

Answer 35

yw :)