In Exercises 17–24, write a formula for the general term (the nth...

Question

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.

1.5, - 3, 6, -12, ...

Accepted Answer

Hey everyone welcome back in this problem. We are asked to work out the formula for the end term of the given geometric sequence and find the eighth term. Using that formula. Okay. And the sequence we're given is 3 -9, 27, -81. So let's first recall the general formula for a geometric sequence. We can write the end term A. N. Is equal to a Our two exponents and -1. A said initial term in our is going to be our common ratio. So let's go ahead and try to find R. And r is going to be the ratio between two consecutive terms. And in a geometric sequence that's going to be consistent in an arithmetic sequence we have the common difference. Okay? We take the previous term. We add the difference to get a new term and in this case we take the old term, we multiply the common ratio to get the new term in a geometric sequence. So let's go ahead and find our common ratio. Okay, well we're gonna take the ratio of two consecutive terms. We're gonna take the second term Divided by the first term. We get R is equal to negative three. Now, that should be consistent for each of those terms. This is a geometric sequence. So are should be the same. Let's just go ahead and check that. We do indeed have a geometric sequence and then we'll continue with our formula. Okay, so if we take the next two terms 27 divided by -9. The previous term. Okay, we again get ours equal to negative three. And if we do it for the final terms were given negative 81 divided by 27. Again we get negative three. Okay and so we have our value of negative three. Let's go ahead and write our formula A. N. is equal to a. Which is again the first term. So we have three Times. Are we just found to be negative three To the exponent N -1. And this is going to be the formula for the nth term. Alright so we've done part one formula for the nth term. Now let's go ahead and find the eighth term. So eight is going to equal three times negative three. Okay and here we have N. Is equal to eight. We have eight minus one. This is gonna give us three times negative. 2187 K. Negative 32 exponents seven. We have an odd power so we have a negative We get negative 6,561 for a third term. Okay so we're looking at the answer choices here we're gonna go with answer D. The formula for the nth term A. M. Is equal to three times negative three to the exponents and minus one and A. A. Is equal to negative 6561. Thanks everyone for watching. I hope this video helped see you in the next one

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence. 1.5, - 3, 6, -12, ...

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