# Thread: Use sigma notation to represent each of the following

1. ## Use sigma notation to represent each of the following

1+6+11+...+(5p-4)

2. ## Re: Use sigma notation to represent each of the following

Originally Posted by poppyisloveinthewind
1+6+11+...+(5p-4)
$\sum _{i=1} ^p 5i - 4$

or, if you prefer:

$\sum _{k=1} ^p 5k - 4$

or even:

$\sum _{j= -2} ^{p-3} 5j+11$

3. ## Re: Use sigma notation to represent each of the following

Originally Posted by Drongoski
$\sum _{i=1} ^p 5i - 4$

or, if you prefer:

$\sum _{k=1} ^p 5k - 4$

or even:

$\sum _{j= -2} ^{p-3} 5j+11$

4. ## Re: Use sigma notation to represent each of the following

Originally Posted by poppyisloveinthewind
No no - not by trial-&-error. As I am very well-versed with the use of the sigma notation, this is nothing to me. It may take you a while to get used to it. Don't be discouraged.

5. ## Re: Use sigma notation to represent each of the following

Originally Posted by Drongoski
No no - not by trial-&-error. As I am very well-versed with the use of the sigma notation, this is nothing to me. It may take you a while to get used to it. Don't be discouraged.
I thought it was +5 for some reason and hence couldnt solve it

6. ## Re: Use sigma notation to represent each of the following

right i think i get it now, the answer is in the question and by using the last value you have to do trial and error, am i right?

7. ## Re: Use sigma notation to represent each of the following

What trial & error?

My 1st and 2nd versions are simply a shorthand for:

(5x1 - 4) + (5x2 - 4) + (5x3 - 4) + . . . + (5xp - 4)

In this case we can express any term of the sum by a formula based on the term number. For this question, the general term is 5n-4 for the nth term. On the other hand, if you want to express 1 + 67 -5 + 1 + 87 +9 - 92 + 109 -55 -13 + 27 + 16 you won't be able to write this down in a sigma notation.

8. ## Re: Use sigma notation to represent each of the following

Originally Posted by poppyisloveinthewind
$\noindent The fact that the terms form an arithmetic progression with \underline{common difference 5} tells us that the general term is of the form 5k+b for some constant b (where k will be our summation index). Then depending on what you want to start your k as, you can find b. E.g. if you want to start with k = 0, then the k = 0 term (starting term in the sum) being 1 means that b will be 1 (since we need 5k + b = 1 when k = 0). This makes the general term 5k+1 (as b = 1). Thus the final term will be when 5k+1 = 5p - 4, i.e. k = p - 1.$

9. ## Re: Use sigma notation to represent each of the following

Originally Posted by poppyisloveinthewind
right i think i get it now, the answer is in the question and by using the last value you have to do trial and error, am i right?
In simple terms, you need to recognise that the sequence is arithmetic, which can be proven by checking that T2 - T1 = T3 - T2.
Ok, now that is done, we need to find Tn. Using the formula for an arithmetic sequence, Tn = a + d(n - 1), we get Tn = 1 + 5(n - 1) = 5n - 4.

Now, we just need to fill in the sigma part! So, on the bottom, we get n = 1, because 1 is the first term (sub n = 1 into Tn to see why). On the top, since it is clear that the last term of the sequence that's being added is the pth term, p is placed on the top of the sigma. Finally, we just put 5n - 4 right next to the sigma (you can put brackets around 5n - 4 if you want to make it unambiguous).

Sigma Question.gif

Hence, no trial and error is needed AT ALL.

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