Problem

Use a formula for $S_{n}$ to evaluate each series…

01:57

Problem 39 Hard Difficulty

Use a formula for $S_{n}$ to evaluate each series.
$$
\sum_{i=1}^{250} i
$$

Answer

31,375

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Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 2

Arithmetic Sequences

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Video Transcript

we're being asked to find the some of this particular Siri's now know this were given the Siris in summation notation. So the first thing we need to figure out Well, how many terms, Aaron, this Siri's? Well, because we're going from I equals 12 I e goes to 50. There are 250 terms, so we're trying to find s up to 50 which tells us that N is equal to 2. 50. Next, we're gonna find Ace of One. To do this, we're gonna substitute one in place of I and R Formula. Well, that's still just gonna be one. And because we're trying to find the some of the 1st 250 terms, let's find it 250 of term. So to do this, we're gonna substitute to on your 50 in place of I, which is just you on your 50. And now that we know n ace of one and a serve to 50 which is kind of like our a seven volume, we're going to use the first of our two summation formulas. So if you recall that formulas s seven is equal to end over to times a serve one was a seven. So it's substitute our values into this formula and it meets school there. So we have s of 2. 50 equals that we're gonna have to 50 divided by two times one plus 250. And now we just need to evaluate Well, 250 divided by two is equal to 1 25 and then we have one plus 250 which is 251. So now we just need to multiply. Well, 125 times 251 is equal to 31,375. And now we found the some of the 1st 250 terms in this particular Siri's. So our answer is 31,375.

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