Determine x and y for the geometric sequence: -2, x, y, 1024, ...

[nineteen]

Determine x and y for each geometric sequence:
-2, x, y, 1024, ...

Normally I would solve this like t2/t1 = t3/t2, but I couldn't for this problem. Thank-you in advance!

 

[Deleted member 4993]

Determine x and y for each geometric sequence:
-2, x, y, 1024, ...

Normally I would solve this like t2/t1 = t3/t2, but I couldn't for this problem. Thank-you in advance!

You were going in the right direction.

You get an equation (in x and y) when you simplify t2/t1 = t3/t2

You get another equation (in x and y) when you simplify t2/t1 = t4/t3

What are those equations?

Another way:

Hint

1024 = (-2) * (-8)^3

 

[pka]

Determine x and y for each geometric sequence:
-2, x, y, 1024, ...
Normally I would solve this like t2/t1 = t3/t2, but I couldn't for this problem. Thank-you in advance!

Here is yet another approach. (First see Mr. Khan's reply#2)
\(\displaystyle a_0=-2,~x=a_0\cdot r,~y=a_0\cdot r^2,1024=a_0\cdot r^3\) knowing that then \(\displaystyle r=~?\)
So find \(\displaystyle x~\&~y\).