Arithmetic sequence, geometric sequence

[sg001]

Homework Statement

Posted this thread earlier but had mis read the given answer. please disregard older thread as I don't know how to delete it!

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

Homework Equations

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

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...

All help is appreciated if someone could point me in the right direction about how to go about this!

 

[tiny-tim]

hi sg001!

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

well, isn't that the answer, then?

 

[sg001]

so just to make sure i understand what's 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)

 

[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 )

 

[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 I am understanding what's goin on

ie 2p = q +r

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

 

[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??

 

[tiny-tim]

hi sg001!

ok so it is

p= 1/2 (q +r)

you mean q = 1/2 (p +r)

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

no, you need an extra equation for each extra term

(eg 5 terms, 3 equations)

 

[sg001]

Okie I understand now.
Thankyou