Write a formula for the general term (the nth term) of each ge...

Question

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. 0.0004, - 0.0004, 0.04, - 0.04, ...

Accepted Answer

Hey, everyone in this problem, we're asked to work out the formula for the nth term of the given geometric sequence. And then to find the eighth term A eight using that formula and the sequence were given 0.0000003 negative 0.00003 and 0.003. OK. So let's think about what a geometric sequence looks like in general. OK? So if we want to write the nth term A N of a geometric sequence, well, this is gonna be equal to A R to the exponent N minus one. Hm where A is the first term an R is our common ratio. OK? When we have a geometric sequence, the ratio between consecutive terms is constant. OK. So the R value is the number that we have to multiply one term by to get the next term. OK? And that's constant for every single term. So let's start by finding R. Well, we wanna take the ratio of consecutive terms. So let's take the first two terms. OK? So we're gonna take the second term and divide it by the term before which is the first term. So negative 0.00003 divided by 0.0000003. And this is going to give us in our value of negative 100. Now this is a geometric sequence. And so again, that ratio is consistent, it's the common ratio. So it's the same for every term. Let's just double check that with the terms we were given. It is indeed the same. Um Just make sure that this is a geometric sequence before we continue. So if we do the same for the next two terms, we get 0.003 divided by the preceding term negative 0.00003. And we find that it is indeed again an R value of negative 100. OK? So we have our is equal to negative 100. OK? The A value again is gonna be the first term. So our a value is just going to be 0.000000. OK. Six zeros three. And what about NN is the number of terms? OK. And so we're talking about finding the eighth term. OK. So in general, a term can be given by A N is equal to 0.0000003 times negative 100 to the N minus one. OK? And in this case, we wanna find a eight which is 0.00000. 03 times negative 100 to the exponent seven, OK, eight minus one. And this gives us a value of negative 30 million. And so the formula for the NTH term A N is equal to 0.0000003 times negative 100 to the exponent N minus one. And the eighth term is negative 30 million K. And so that is going to be answer B thanks everyone for watching. I hope this video helped see you in the next one.

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. 0.0004, - 0.0004, 0.04, - 0.04, ...

Key Concepts

Geometric Sequence

General Term Formula of a Geometric Sequence

Finding Specific Terms Using the General Formula

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Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence. 0.0004, - 0.0004, 0.04, - 0.04, ...

Key Concepts

Geometric Sequence

General Term Formula of a Geometric Sequence

Finding Specific Terms Using the General Formula

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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. 0.0004, - 0.0004, 0.04, - 0.04, ...