Compute $(\sum_{i=1}^5 x_i)+10$ with given $x_i$'s

Question

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.

Answer 1

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

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

Answer 2

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.