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So I need help computing the following sum.

Question: Suppose $ x_1 = 5, x_2 = −3, x_3 = 7, x_4 = 8,$ and $x_5 = 2$. Compute the following sum.

$(\sum_{i=1}^5 x_i)+10$ where the upper limit is 5, and the lower limit is $i = 1$. The expression is $(x_i) + 10$. keep in mind the $+10$ is outside the brackets.

What I think:

Since we are given the values for each $x$ $(5,-3,7,8,2)$, i am assuming that it would be $(5+10) + (-3+10)$ so and so forth.

Now that is what I think. I don't know the correct answer. So can someone please help me figure it out.

Thank You.

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    Addition does not distribute like that ($x+(y+z) \neq (x+y) + (x+z)$). The parentheses are emphasizing that $\sum_{i=1}^5 x_i$ should be computed first and then to that we add $10$. What is the value of $\sum_{i=1}^5 x_i$ going to be? – 2017-02-26
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    In the edit you added another question,you shouldn't do that,anyway I would suggest you to try it yourself and tell us where you are stuck(preferably in another question). – 2017-02-26
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    Please do not use pictures for critical portions of your post. Pictures cannot be searched and are inaccessible to those using screen readers. Ref: http://meta.math.stackexchange.com/a/20529/290189 – 2017-02-27

2 Answers 2

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As you say, the addition of $10$ is outside the brackets. So you make the sum first:

$(\sum_{i=1}^5 x_i)+10= (5+-3+7+8+2)+10 = 19+10=29$

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Be careful, as you said, the $+10$ is outside of the brackets: $$(\sum_{i=1}^{5}x_{i})+10.$$

Since the order of operations tell us to compute expressions within parenthesis first, we want to first compute the sum $\displaystyle\sum_{i=1}^{5}x_{i}$ and then add $10$ to the result.

On the other hand, if we were given $$\sum_{i=1}^{5}(x_{i}+10)$$ then we would have the following sum $$(x_{1}+10)+(x_{2}+10)+(x_{3}+10)+(x_{4}+10)+(x_{5}+10).$$ Here, the parenthesis are implying that the $+10$ is in each term of the sum.

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    Thank You very much but a quick question, If there was a Square outside the brackets, then we would still do the sum first then the Square of the total sum. Correct?/? – 2017-02-26
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    Yes, if you had $$\big[\sum_{i=1}^{5}x_{i}\big]^{2},$$ you would indeed compute $\sum_{i=1}^{5}x_{i}$ first, and then square the result. – 2017-02-26
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    Hey Can you help me with this. can you check the updated question. please and thank you. – 2017-02-26
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    @JainamPatel No!!! See [this post about question edit](http://meta.math.stackexchange.com/a/25490/290189) on meta.mathse by quid: "As a rule a question should not be a moving target, and to alter it in such a way as to render existing answers wrong or even just incomplete is discouraged. It is alright to rollback such edits and to ask OP to ask a new question." – 2017-02-27