Arithmetic Sequence for homework,im also new to this website

[Digital Genius]

Homework Statement

a, b and c are consecutive numbers in a geometric sequence, where a+b ≠ 0 and b+c ≠ 0

* "/" means divide *

Show that 2ab/a+b, b and 2bc/b+c are consecutive terms in an arithmetic sequence

The Attempt at a Solution

i know this has something to do with it...

a,b,c GP

Show 2ab/a+b, b, 2bc/b+c ...

T1, T2, T3 of AP

T2-T1=T3-T2

b-(2ab/a+b)=(2bc/b+c) - b

b2 = ac

 

[LCKurtz]

Homework Statement

a, b and c are consecutive numbers in a geometric sequence, where a+b ≠ 0 and b+c ≠ 0

* "/" means divide *

Show that 2ab/a+b, b and 2bc/b+c are consecutive terms in an arithmetic sequence

If you mean 2ab/(a+b), b , 2bc/(b+c) write it that way. Parentheses matter.

The Attempt at a Solution

i know this has something to do with it...

a,b,c GP

Show 2ab/a+b, b, 2bc/b+c ...

T1, T2, T3 of AP

T2-T1=T3-T2

b-(2ab/a+b)=(2bc/b+c) - b

b2 = ac

You haven't used the fact that a,b,c are a GP. That means $b=ar^2,~c=ar^3$. Use that. Or you can divide that last equation by ab, assuming neither are zero.

 

[Ray Vickson]

Homework Statement

a, b and c are consecutive numbers in a geometric sequence, where a+b ≠ 0 and b+c ≠ 0

* "/" means divide *

Show that 2ab/a+b, b and 2bc/b+c are consecutive terms in an arithmetic sequence

The Attempt at a Solution

i know this has something to do with it...

a,b,c GP

Show 2ab/a+b, b, 2bc/b+c ...

T1, T2, T3 of AP

T2-T1=T3-T2

b-(2ab/a+b)=(2bc/b+c) - b

b2 = ac

What you wrote means
$$\frac{2ab}{a} + b \text{ and } \frac{2bc}{b}+c$$
Is that what you wanted, or did you want
$$\frac{2ab}{a+b} \text{ and } \frac{2bc}{b+c}?$$
Parentheses are important: if you mean $\frac{A}{B+C}$ you need to write it in text as A/(B+C).