Tuesday

September 16, 2014

September 16, 2014

Posted by **Sidney** on Monday, February 14, 2011 at 3:06pm.

- math -
**Reiny**, Monday, February 14, 2011 at 3:17pmlet the sequence be

3 a b 9

then b/a = 9/b and b-a = 9-b

from the first...

b^2 = 9a

a = b^2/9

from the second...

a = 2b-9

so b^2/9 = 2b-9

b^2 = 18b - 81

b^2 - 18b + 81 = 0

(b-9)(b-9) = 0

b = 9

then a = 9

sum of these two numbers is 18

- math -
**Sidney**, Monday, February 14, 2011 at 3:23pmThanks, this helped a lot! :)

- ERROR - math -
**Reiny**, Monday, February 14, 2011 at 3:40pmMy solution is wrong, I misread the question.

should be

b/a = a/3 ---- a^2 = 3b

b-a = 9-b ---> a = 2b-9

then (2b-9)^2 = 3b

4b^2 - 36b + 81 = 3b

4b^2 -39b + 81 = 0

b = (39 ± √225)/8

= 27/4 or 3

if b=3, then a = 3, sum of those two is 6

if b = 27/4, then a = 9/2 or 4.5 , their sum is

however.... 3 3 3 9 does not satisfy the original condition, while

3 , 9/2 , 27/4 , 9 does work

so the 2 numbers inserted are 9/2 and 27/4

or 4.5 and 6.75

their sum is 11.25

sorry about the previous post.

- math -
**Sidney**, Monday, February 14, 2011 at 3:49pmAh, okay I see. Thanks for correcting it.

**Answer this Question**

**Related Questions**

Algebra/Number Theory - In a sequence of four positive numbers, the first three ...

Math (Geometric Progression) - 5 distinct positive reals form an arithmetic ...

Math - 5 distinct positive reals form an arithmetic progression. The 1st, 2nd ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

Maths - 1..The first 2 terms of a geometric progression are the same as the ...

Arithmetic - The first, second and third terms of a geometric progression are 2k...

Pre-Calculus - Three numbers whose sum is 15 are in an arithmetic progression. ...

Algebra - Determine whether each sequence is arithmetic or geometric. Find the ...

math - Determine whether each sequence is arithmetic or geometric. Find the next...