# Math

posted by .

I have to find the relationship between these sequences, and express a generality. Could you help please.

1 + 3 + 5 + 3 + 1 = 3^2 + 2^2
1 + 3 + 5 + 7 + 9 + 7 + 5+ 3 + 1 = 5^2 + 4^2
1 + 3 + 1 = 2^2 + 1^2

I'm thinking sum of consecutive primes can be expressed in squares? The numbers add up. What's the generality?

Thanks

• Math -

First of all, did you know that the sum of the first n odd numbers is n^2 ?

e.g.
1+3+5+7+9+11 = 6^2 = 36

So when you look at your sequences, they are actually made up of the addition of the sum of n odd number plus the addition of (n-1) odd numbers

(1+3+5+7+9) + (1+3+5+7) = 5^2 + 4^2

If you know how to express sigma notation you could do
sigma(2i-1) from i=1 to n + sigma(2i-1) from 1 to n-1 = n^2 - (n-1)^2

• correction - maths -

last line should have said :
sigma(2i-1) from i=1 to n + sigma(2i-1) from 1 to n-1 = n^2 + (n-1)^2

• Math -

Thanks Reiny,

Yes, I spotted that it dosen't work for any run of primes, but it does up to 9. I'm afraid i don't really follow your explanation!

Charlie

• Math -

ok, look at this patters

sum of 1 odd number = 1 = 1^2
sum of 2 odd numbers = 1+3 = 4 = 2^2
sum of 3 odd numbers = 1+3+5 = 9 = 3^2
sum of 4 odd numbers = 1+3+5+7 = 16 = 4^2
...
sum of n odd numbers = 1+3+...+ (2n-1) = n^2
( 2n-1) is the general expression for an odd number.

this has nothing to do with primes.
Why do you say it works only up to 9, it works for the sum of odd numbers up to any value you want.
e.g.
1+3+5+7+9+11+13+15+17+19 = 10^2 = 100.
They were the first 10 odd numbers.

now look again at your second example of
1+3+5+7+9+7+5+3+1
=1+3+5+7+9 + (1+3+5+7)
= sum of first 5 odd numbers + sum of the first 4 odd numbers
= 5^2 + 4^2

## Similar Questions

1. ### pre calc

given x=t^2 and y=t-2 find a relationship between x amd y( express y in terms of x) is the relationship a function
2. ### Math

I'm learning series and sequences (grade 11). Please check that my steps show I understand what I'm doing/the concept and my answer as well: 5. The consecutive terms of an arithmetic sequences are 3.6, y, 8.2. Find the value of y. …
3. ### Math Ms. Sue please

7. Which of the following types of information is NOT suited for display on a scatter plot?
4. ### Biology

When making comparison of sequences where some are whole genome sequences while others are partial genome sequences, or a specific glycoprotein sequence, How is it that we are able to make comparisons from these sequences if they all …
5. ### Math

1) Describe the relationships you discovered in the Fibonacci sequences. 2) what strategies did you use to search for relationships. 3)how many examples of a relationship do you need to check before you start to believe that the relationship …

Which of the following types of information is NOT suited for display on a scatter plot?