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
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!
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
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 πŸ₯ΊπŸ˜‡!! 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 πŸͺ*
Answered by work hard play hard
Great job ReinyπŸ‘πŸ‘πŸ‘πŸ‘!!
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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