Question

if x-5, 2x, and 4x+6 are the first 3 terms of an arithmetic sequence, find x and the values of the three terms

Answer 1

what is \(2x-(x-5)\)?

Answer 2

x-5

Answer 3

wait x+5

Answer 4

yes

Answer 5

so the difference between the first two terms is \(x+5\)

Answer 6

now what is \(4x+6-2x\)?

Answer 7

2x-6

Answer 8

i agree
and since it is arithmetic, the differences must be the same
to find \(x\) solve \[x+5=2x-6\]

Answer 9

x=11

Answer 10

that is what i get too

Answer 11

now that you know \(x=11\) finding the value of the first 3 terms should be easy enough right?

Answer 12

\[a _{1}=6\]
\[a _{2}=22\]
\[a _{3}=50\]

Answer 13

that doesn't seem right

Answer 14

no it doesn't does it

Answer 15

can we try
\[2x=(x-5)+(2-1)(x+5)\]

Answer 16

that doesn't work out either

Answer 17

hold on let me think see if i can figure out what is wrong with this method
common differences must be equal

Answer 18

oh cause i am an idiot

Answer 19

i wrote \[x+5=2x-6\] but it really should have been \[x+5=2x+6\] doe

Answer 20

since \(4x+6-2x=2x+6\)

Answer 21

works now i bet

Answer 22

x=-1

Answer 23

yes, now try it, see if it works

Answer 24

thank you