In Exercises 55–60, express each sum using summation notation. Us...

Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+(a+d)+(a+2d)+⋯+ (a+nd)

Accepted Answer

Welcome back. I am so glad you're here. We are given the following some. It is P plus Q plus P plus three Q plus P plus five Q etcetera? All the way up to this last one, P plus two N minus one times Q. And we're asked to rewrite this in summation notation. Well, we recall from previous lessons that summation notation is this big sigma and on top of the sigma is our upper limit. Or in other words it's going to be the last value of n. On the bottom beneath the sigma. We're going to have an index and looking at our answer choices. They've chosen K to be the variable for the index and that's going to be equal to the lower limit or the first value of N. And then to the right of sigma is going to be the formula. And the formula will be in terms of our index which is K. So how do we figure out these three parts the upper limit? The formula and the lower limit? Well, starting with the upper limit, we can look at that last term here in the some P plus two and minus one times Q. And we can see that the upper limit here is going to be an that's as high, that's the highest number that we get here. It's the variable end. And now we can use that. And because that's the upper limit where we can substitute K. N for N. So we'll have P plus two K minus one times Q. And that's going to be our formula P plus because it's in terms of K2K - times cute. And then the last question is just, what's the lower limit? What's the first value that we have in for our variable? And we can do that by setting our formula equal to our first term here in our sum equal to P plus Q. Now we can solve for K. And that will give us our lower limit. So we can start off by subtracting P from both sides, which will leave us with two k minus one times Q equals Q. Next we can divide both sides by Q and that will give us two k minus one equals one. We can add one to both sides and that will give us two K equals two And divide both sides by two. And the lower limit of R. K value when we plug it in for that first term here and set that equal to our formula K equals one. So we look at our answer choices and this matches with answer choice. A Well done. We'll catch you on the next one.

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+(a+d)+(a+2d)+⋯+ (a+nd)

Key Concepts

Summation Notation

Arithmetic Sequence

Index of Summation

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