Question

three numbers whose common difference is 5 are in an arithmetic sequence. if the first number is left unchanged, and 1 is subtracted from the second, and 2 is added to the third, the resulting three numbers are in a geometric sequence. find the three original numbers and the geometric sequence.

Answer 1

Did you get an answer yet?

I think I solved it, if you want help solving it.

Answer 2

I still can't figure it out

Answer 3

let the numbers be a-5,a,a+5
new numbers are a-5,a-1,a+5+2 or a-5,a-1,a+7
because they are in G.P
\[\left( a-1 \right)^2=\left( a-5 \right)\left( a+7 \right)\]
calculate a and then the numbers

Answer 4

@sshayer I don't understand why you have to square (a-1) can you explain?

Answer 5

if a,b,c are in G.P then \[\frac{ b }{ a }=\frac{ c }{ b }~or~b^2=ac\]

Answer 6

I got \[a ^{2}-2a+1 = a ^{2}+2a+35\]

Answer 7

good
take all the terms with a and a^2 on one side and constant terms on other side and find a

Answer 8

it is -35

Answer 9

-5*7=-35

Answer 10

oops

Answer 11

9=a

Answer 12

now find the original numbers

Answer 13

4,9,14

Answer 14

correct

Answer 15

now find the numbers of G.P

Answer 16

4,8,16

Answer 17

correct well done.

Answer 18

thank you

Answer 19

yw