Question

Find the four arithmetic means between -21 and -36.

Answer 1

@Vocaloid

Answer 2

-21 is the first term
-21+d is the next term right after the first term. The d is some unknown common difference

add d to the last term, -21+d, to get
(-21+d)+d = -21+d+d = -21+2d

Answer 3

so far we have

first term: -21
second term: -21+d
third term: -21+2d

what would be the fourth term?

Answer 4

-21 + 3d?

Answer 5

correct, how about the fifth term?

Answer 6

-21 + 6d

Answer 7

you add d to the fourth term

fifth term = (fourth term) + d

Answer 8

4d

Answer 9

yep, so we have this summary so far

first term: -21
second term: -21+d
third term: -21+2d
fourth term: -21+3d
fifth term: -21+4d

Answer 10

the second term through the fifth term will be the middle four terms

the last term, the sixth term, we need is

sixth term = (fifth term) + d
sixth term = (-21+4d) + d
sixth term = -21+5d

Answer 11

first term: -21
second term: -21+d
third term: -21+2d
fourth term: -21+3d
fifth term: -21+4d
sixth term: -21+5d

Answer 12

the sixth term is also equal to -36 which is given at the top, so,

sixth term = -21+5d
-21 + 5d = -36

solve for d and tell me what you get

Answer 13

one thing, how is the 6th term equal to -36?

Answer 14

d = -3

Answer 15

we have this sequence at first