Find the sum of the first 15 terms of the geometric sequence: 5, ...

Question

Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135

Accepted Answer

Welcome back. I'm so glad you're here. We've got a geometric sequence. Three negative 21 147 negative 1029 so on. And we are to find the sum of the first seven terms of this sequence. Well this is exciting because we recall from previous lessons that we've got a formula for this. The formula is the sum of the number of how many terms that we're looking for equals in the numerator we've got the value of the first term or a sub one times one minus the ratio raised to that end value and parentheses divided by and in the denominator we have one minus that ratio again or are. So now let's just figure out what our a sub one hour N. And our our values are a sub one. That's the value of the first term in the sequence. The first term here is three. So a sub one equals three. And well that's the number of the last term that we're looking for to add together. And we are looking for the first seven terms, so n equals seven. Our takes a little bit more work. We're going to choose any two sequential numbers from our sequence. Um I'll just choose the first two numbers and we're going to take the second of those two. So that be a sub two and divided by the one immediately preceding it. So that would be a sub one in this case. So a sub to hear the second term is negative 21 divided by the term immediately preceding it divided by three, negative 21 divided by three is negative seven so R equals negative seven. Now let's just plug everything in the sum of the first in or seven terms in our sequence equals the value of the first term, or a sub one which is three times one minus R ratio, which is negative seven, Raised to the end value which is seven. Close parentheses, divided by one minus R ratio again, which is negative seven. We plug all that into a calculator and that gives us the answer of 308,829. We look at our answer choices in that matches with answer choice d. While done we'll catch on the next one.

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