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.

Answer 1

(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

Answer 2

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!

Answer 3

very, very, very correct

Answer 4

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Answer 5

Very very good!!
That helped me a lot

Answer 6

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Answer 7

Excellently wonderful, bravo reiny, keep it up.

Answer 8

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 🍪*

Answer 9

Great job Reiny👏👏👏👏!!

Answer 10

Great work! Thanks alot.

Answer 11

Great

Answer 12

Reiny you are very very good at maths pls keep it up

Answer 13

Verry great Reiny keep up the good work.

Answer 14

Bravo it really helped me

Answer 15

I don't understand how a (1.125) = 9

Answer 16

So I don't understand from there

Answer 17

I don't really understand how you gotar^3(r-1)

Answer 18

Thanks Renny