# Homework Help: Arithmetic sequence, geometric sequence

1. Feb 25, 2012

### sg001

1. The problem statement, all variables and given/known data

Write down the condition for the numbers p, q, r to form an arithmetic sequence & geometric progression.

2. Relevant equations

\ a_n = a_1 + (n - 1)d, ???

3. The attempt at a solution
Have no idea, tried looking for similar examples on the net but they all seem to include numbers that are euidistant ie 5, 7, 9, 11......

2. Feb 25, 2012

### tiny-tim

hi sg001!
well, isn't that the answer, then?

3. Feb 25, 2012

### sg001

so just to make sure i understand whats goin on here.../

If i had the same question but now with a,b,c,d,e,f.

The conditions for arithmetic sequence containing these numbers would be...

a = 1/5(b+c+d+e+f)

4. Feb 25, 2012

### tiny-tim

i] nooo

ii] just do it for p q and r …

what is the equation that p q and r (only) have to satisfy?

(in other words: translate what you've already said into an equation )

5. Feb 25, 2012

### sg001

ok so it is

p= 1/2 (q +r)

but is this the case for questions with a larger amount of terms

ie p,q,r,s,t,u

where i can say to satisfy an arithmetic sequence

p= 1/5 (q +r+ s+t+u)

because this is how im understanding whats goin on

ie 2p = q +r

& 5p = q + r +s +t +u

6. Feb 25, 2012

### sg001

Or does it only work because q is the middle term
Therefore p & r are equidistant from q .
Hence, q = 1/2 (p + r)

So it will only work with an odd amount of numbers ie a,b,c or a,b,c,d,e
By working it out simply that is??

7. Feb 25, 2012

### tiny-tim

hi sg001!
you mean q = 1/2 (p +r)
no, you need an extra equation for each extra term

(eg 5 terms, 3 equations)

8. Feb 25, 2012

### sg001

Okie I understand now.
Thankyou