Problem

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

02:22

Problem 36 Hard Difficulty

Use a formula for $S_{n}$ to evaluate each series.
$$
\sum_{i=1}^{17}(3 i-1)
$$

Answer

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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 s seven for the Given. Siri's well know this that are sequins or sorry are Siri's is given the signal station. So let's look at the first part we're going from I equals 1 to 17 which means we're trying to find the some of the 1st 17 terms in the sequence. So never words were trying to find a sub 17 which means that end is equal to 17. All right, well, the first thing we need is we need to know the first time in the sequence. So to do this, we're gonna substitute one in place of I in our formula. So we're gonna have three times one minus one. Well, three times one, this three and three minus one is too. So the first thing is to now the last thing going to do is find the 17th term in the sequence, which is kind of like our A seven value. To do this, we're gonna substitute 17 in place of I and R formula. So I'm gonna have three times 17 minus one. Well, three times 17 is 51 51 minus one is 50. Well, now, don't know n ace of one in a sea of 17. We can use the first of our summation formulas to find us of 17. So remember, our formula is Esa Ben is equal to end over to times a serve one plus ace event, which, in this case, is a step 17. So this substitute our three values into our formula. So I gotta have s of 17 equals. Then we're gonna have 17 divided by two times a sublime, which is to plus a seven, which is 50. In this case, it's our seven teams turn, and now we just need to simplify. Well, 17 divided by two is equal to 8.5 and two plus 50 is 52. So now we just need to multiply 8.5 by 52 which is equal to 442. So great. Now we found the some of the sequence. So s up 17 is equal of 442

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