the first 3 term of a geometric progression are
k-4, 2k-4, 4k+4.
what is the value of k?
can someone help please!
in any geometric progression any term divided by its previous term gives you the common ratio, so ....
(2k-4)/(k-4) = (4k+4)/(2k-4)
cross-multiply and proceed.
I comes out nice, the square term cancels.
how do i cross multiply this?i get confused easiy when doing cross multiply in division...
(2k-4)(2k-4) = (k-4)(4k+4)
4k^2 - 16k + 16 = 4k^2 - 12k - 16
-4k = -32
k=8
ooh so you times it by the opposite!silly me...
Thank you soo much!!
yes, in general
a/b = c/d -----> bc = ad
try it with equivalent fractions
we know 2/3 = 10/15
then 2*15 = 3*10 ...true!
That's correct! When solving equations involving fractions, you can apply cross-multiplication. To cross-multiply, you multiply the numerator of one fraction by the denominator of the other fraction. In this case, you have:
(2k-4)/(k-4) = (4k+4)/(2k-4)
To cross-multiply, you multiply (2k-4) by (2k-4) and multiply (k-4) by (4k+4):
(2k-4)(2k-4) = (k-4)(4k+4)
Expanding both sides, you get:
4k^2 - 16k + 16 = 4k^2 - 12k - 16
Now, simplify and solve the equation:
4k^2 - 4k^2 - 16k + 12k = -16 + 16
Combining like terms, you have:
-4k = -32
Dividing both sides of the equation by -4, you get:
k = 8
So the value of k is 8.