Asked by AREMU
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
Answered by
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
Answered by
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!
Answered by
jane
very, very, very correct
Answered by
Bolton
Reiny u are very very good
Answered by
Brigs
Very very good!!
That helped me a lot
That helped me a lot
Answered by
Daniel.
Excellently wonderful, bravo reiny, keep it up.
Answered by
Daniel.
Excellently wonderful, bravo reiny, keep it up.
Answered by
Reiny
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*
Answered by
work hard play hard
Great job Reinyππππ!!
Answered by
Taiwo faruk segun
Great work! Thanks alot.
Answered by
Gabriel
Great
Answered by
Olumide
Reiny you are very very good at maths pls keep it up
Answered by
Valentine
Verry great Reiny keep up the good work.
Answered by
Gillian
Bravo it really helped me
Answered by
Promise
I don't understand how a (1.125) = 9
Answered by
Promise
So I don't understand from there
Answered by
Temidayo
I don't really understand how you gotar^3(r-1)
Answered by
Deb damil
Thanks Renny
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