Find the value of y that makes y + 4, 6, y, ... an arithmetic sequence.

Question

arithmetic sequences

Answer 1

to be arithmetic then you have to 'add' the same number each time to get the next value, call this number x

then (y+4)+x=6 and 6+x=y

solve the 2nd equation for x and x=y-6

substitute this into the first equation for x and (y+4) +(y-6)=6

combine like terms and 2y-2=6

add 2 to both sides and 2y=8

divide both sides by 2 and y=4