Question
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.
Answers
Scott
(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
x^2 + 18 x + 81 = x^2 + 22.5 x
81 = 4.5 x
a1, a2, 18, 27, 40.5
Reiny
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!
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!
jane
very, very, very correct
Bolton
Reiny u are very very good
Brigs
Very very good!!
That helped me a lot
That helped me a lot
Daniel.
Excellently wonderful, bravo reiny, keep it up.
Daniel.
Excellently wonderful, bravo reiny, keep it up.
Reiny
Thank you guys 🥺😇!! 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 🍪*
work hard play hard
Great job Reiny👏👏👏👏!!
Taiwo faruk segun
Great work! Thanks alot.
Gabriel
Great
Olumide
Reiny you are very very good at maths pls keep it up
Valentine
Verry great Reiny keep up the good work.
Gillian
Bravo it really helped me
Promise
I don't understand how a (1.125) = 9
Promise
So I don't understand from there
Temidayo
I don't really understand how you gotar^3(r-1)
Deb damil
Thanks Renny