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What is 11∑n=1(98−2n) equal to?

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What is 11∑n=1(98−2n) equal to?

Apr 27, 2018

#1
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What are you trying to sum up? Can you explain it in plain English? Because your summation formula doesn't make sense the way it is written. If you want to sum up: 98 - 2n, from n=1 to 11, then it should be written like this: ∑[98 - 2n], from n= 1 to 11.

Apr 27, 2018
#2
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This is a finite summation of an arithmetic series because each subsequent term is simply subtracting two. We can figure out what the first term of the sequence is. Of course, you could just add up all the terms from 1 to 11, but it is probably better to use or derive a formula. In order to find the sum of an arithmetic sequence, you must find three values:

• a(the first term)
• a(the last term)
• n (number of terms)

We know that the first term of a summation is when the variable, n, equals its first possible value, which is one, in this case.

 $$a_1=98-2*1=96$$

an can be found by using a formula.

 $$a_n=a_1+d(n-1)$$ Of course, we already know what a1 equals. We know the common difference is -2. The coefficient of the variable indicates this information. $$a_{11}=96-2(11-1)$$ Time to simplify! $$a_{11}=96-20$$ $$a_{11}=76$$

What about the number of terms? Well, this can be determined using the term numbers indicated in summation formula.

$$n=11-1+1=11$$

Let's put all this information together and use the formula to find the sum.

$$S_n=n\left(\frac{a_1+a_n}{2}\right)$$

 $$S_n=n\left(\frac{a_1+a_n}{2}\right)$$ Plug in the values and simplify. $$S_{11}=11(\frac{96+76}{2})$$ $$S_{11}=946$$
Apr 28, 2018