What is the 7th term of the geometric sequence where a1 = 1024 and a3 = 64?

Question

solomonzelman · Answer

$\large\color{blue}{ \bf a_{1} \times r=a_{2}  }$  and  $\large\color{blue}{ \bf a_{3} \div r=a_{2}  }$

knowing that they are both equal to  a2,  (and knowing a1 and a3) can you find the r ?

anonymous · Answer

1,024 x r = a_2 
64/r = a_2

So... my guess is to divide 1,024 by 64

So the answer is 0.0625

solomonzelman · Answer

We can set the equations as,   $\large\color{blue}{ \bf   a_1 \times r = a_3 \div r   }$ because each side gives the value of the second term.

anonymous · Answer

Thank you again :) I just need to be shown the formula and see what matches to what and I think I'm set! :) Could you help me with one last question?

solomonzelman · Answer

$\large\color{blue}{ \bf  2014 \times r = 64 \div r   }$

$\large\color{blue}{ \bf  2014 \times r^2 = 64   }$

$\large\color{blue}{ \bf  r^2 = \frac{64}{2014}   }$

solomonzelman · Answer

So the ratio is the square root of that fraction... I don't like dealing with not-perfect squares -:(

anonymous · Answer

oh! So that wasn't the correct answer?

solomonzelman · Answer

https://www.google.com/#q=64+divided+by+2014 and then square root of that, or you can work with the exact value. Whatever you prefer.

anonymous · Answer

ok thank you :) you're a lifesaver!

solomonzelman · Answer

Lets work with an exact value.

But before can you answer one question ?

solomonzelman · Answer

Do you understand

why   (ready? pay attention!!! )  are there going to be different ratios, and why don't we have to worry about this (and we can just work with the positive ratio) ?

solomonzelman · Answer

2 different ratios...