Arithmetic sequence, geometric sequence

In summary, the conversation discusses the conditions for numbers to form an arithmetic sequence and geometric progression. The solution involves finding equidistant numbers and translating it into an equation. It is necessary to have an extra equation for each additional term in the sequence.
  • #1
sg001
134
0

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!
 
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  • #2
hi sg001! :wink:
sg001 said:
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? :smile:
 
  • #3
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)
 
  • #4
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 :wink:)
 
  • #5
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
 
  • #6
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
hi sg001! :smile:
sg001 said:
ok so it is

p= 1/2 (q +r)

you mean q = 1/2 (p +r) :wink:
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)
 
  • #8
Okie I understand now.
Thankyou
 

1. What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference and is denoted by d.

2. How do you find the nth term of an arithmetic sequence?

The general formula for finding the nth term of an arithmetic sequence is: an = a1 + (n-1)d, where an represents the nth term, a1 represents the first term, and d represents the common difference.

3. What is a geometric sequence?

A geometric sequence is a sequence of numbers in which the ratio between any two consecutive terms is constant. This constant ratio is called the common ratio and is denoted by r.

4. How do you find the sum of an arithmetic sequence?

The sum of an arithmetic sequence can be found using the formula: Sn = (n/2)(a1 + an), where Sn represents the sum of the first n terms, n represents the number of terms, and a1 and an represent the first and nth terms, respectively.

5. How can you determine if a sequence is arithmetic or geometric?

To determine if a sequence is arithmetic or geometric, you can look at the differences or ratios between consecutive terms. If the differences between consecutive terms are constant, then the sequence is arithmetic. If the ratios between consecutive terms are constant, then the sequence is geometric.

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