determine the value of 'x' that makes each sequence arithmetic.
d) x-4, 6, x
e) x+8, 2x+8, -x

Question

determine the value of 'x' that makes each sequence arithmetic.
d) x-4, 6, x
e) x+8, 2x+8, -x

turingtest · Answer

if each term in the sequence is equidistant from the next we can write the difference between each term mathematically and set them equal$$6-(x-4)=x-6$$solve for x

turingtest · Answer

...because each term is equidistant from the next in an arithmetic progression

anonymous · Answer

so then
6-x+4=x-6
10-x=x-6
10+6=x+x
16=2x
8=x

yay ! thanks :)

turingtest · Answer

welcome :D
same deal for the next one as well

anonymous · Answer

so it would be 2x+8 - (x+8) = -x 
right ?

turingtest · Answer

you forgot the difference of the last terms
2x+8 - (x+8) = -x - (2x +8)

anonymous · Answer

nvm,i got it,thanks man! its -2

turingtest · Answer

call the entries of the series$$E_1,E_2,E_3$$if it is an arithmetic progression we have$$E_2-E_1=E_3-E_2$$is the idea...
again, welcome!