Question

find the missing terms of each arithmatic sequence
2,a2,a3,a4,-22,...
please help!

Answer 1

let a1 and a4 be the first and fourth terms respectively

Answer 2

so

a1 = 2
a2 = unknown
a3 = unknown
a4 = -22

Answer 3

if d is the common difference, then to go from a1 to a2, you add on d like this

a2 = a1 + d

and to go from a2 to a3, you add on d again

a3 = a2 + d

and you repeat to get a4

a4 = a3 + d

Answer 4

making sense so far?

Answer 5

yea ok so i just need to do at as missing to and thn common sence shows the 4th term

Answer 6

but im not sure how to get the common diffrence part

Answer 7

so this means

a2 = a1 + d

a2 = 2 + d ... plug in a1 = 2

-------------

a3 = a2 + d

a3 = (2+d) + d ... plug in a2 = 2+d

a3 = 2+2d

-------------

a4 = a3 + d

a4 = (2+2d) + d ... plug in a3 = 2+2d

a4 = 2 + 3d

Answer 8

because a4 = 2 + 3d and because a4 = -22, we can say

a4 = 2 + 3d

-22 = 2 + 3d

d = ??

Answer 9

-8?

Answer 10

good

Answer 11

so

a2 = a1 + d

a2 = 2 + (-8)

a2 = 2 - 8

a2 = -6

Answer 12

what is a3?

Answer 13

so i just add -8 to each term?

Answer 14

-14?

Answer 15

correct, and yes a3 = -14

Answer 16

ok so i got 2,-6,-14,-22 but i still have a4 between -14 and -22?

Answer 17

what do you mean when you say "but i still have a4 between -14 and -22"

Answer 18

it says the correct answers are -4,-10,-16 i just need to show my work

Answer 19

oh i messed up

Answer 20

the question is:
2,a2,a3,a4,-22...

Answer 21

I should have gone to a5, not a4

Answer 22

solve for d

a5 = a1 + 4d

-22 = 2 + 4d

d = ??

Answer 23

-6

Answer 24

so

a2 = a1 + d

a2 = 2 + (-6)

a2 = 2 - 6

a2 = -4

Answer 25

ok i got it thnx a bunch

Answer 26

you're welcome