The fifth of an exponential sequence (GP) is greater than the fourth term by 13.5 and fourth term is greater than the thrid by 9.Find:common ratio and the first term.
ar^4 - ar^3 = 13.5
ar^3(r - 1) = 13.5 **
ar^3 - ar^2 = 9
ar^2(r-1) = 9 ***
divide ** by ***
r = 13.5/9 = 1.5
sub into ***
a(1.5)^2 (1.5-1) = 9
a(1.125) = 9
a = 9/1.125 = 8
first term is 8, common ratio = 1.5 or 3/2
check:
the terms are:
8, 12, 18, 27, 40.5, ...
term5 - term4 = 40.5-27 = 13.5 , good!
term4 - term3 = 27-18 = 9 , as it should be!
Reiny u are very very good
Thank you guys π₯Ίπ!! I know this was written 3 years ago, and thanks for telling me how good I am at math. This is very very late, but thanks I appreciate it. *Hands out cookies πͺ*
Very very good!!
That helped me a lot
very, very, very correct
Great job Reinyππππ!!
Excellently wonderful, bravo reiny, keep it up.
Great work! Thanks alot.
Bravo it really helped me
I don't understand how a (1.125) = 9
So I don't understand from there
I don't really understand how you gotar^3(r-1)
Thanks Renny
Excellently wonderful, bravo reiny, keep it up.
Great
Reiny you are very very good at maths pls keep it up
Verry great Reiny keep up the good work.
(x + 9) / x = (x + 22.5) / (x + 9)
x^2 + 18 x + 81 = x^2 + 22.5 x
81 = 4.5 x
a1, a2, 18, 27, 40.5