In Exercises 25–27, use the formula for the sum of the first n te...

Question

In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.  The  is a summation, refer to the textbook.

Accepted Answer

Welcome back. I'm so glad you're here. We've got an arithmetic sequence here and we want to find the sum of the 1st 25 terms of it. Well we can use this S sub N formula. This summation of an arithmetic sequence for the first n number of terms and in this case the end number of terms we're looking for is 25 of them. So the formula we recall from previous lessons is N over two times a sub one. That's the first term plus a sub N. That's as high as we're going. So we're going up to 25. So we've got 25 divided by two times our first term plus the 25th term. And now let's just figure out a sub one in a sub 25. The first and 25th terms. A sub one means that in our or I minus seven formula here, we're going to plug a one in for I so four times one minus seven or in other words four minus seven or in other words negative three. Now let's do the same thing for our a sub 25 or our 25th term, plug a 25 in for I Four times 25 -7 or in other words 100 -7. Or in other words 93. Now we can just do the algebra we've got 25/2 times negative three plus 93. Let's do the parentheses first negative three plus 93 is Times 25/2. You can put that into a calculator and that's going to give us 1,125. We look at our answer choices and that matches with answer choice. D Well done, we'll catch you on the next one.

In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. The is a summation, refer to the textbook.

Key Concepts

Arithmetic Sequence

Sum of the First n Terms

Formula Derivation

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