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# Extending geometric sequences

CCSS.Math:

## Video transcript

so we're told that the first four terms of a geometric sequence are given so they give us the first four terms and say what is the fifth term in the sequence and like always pause the video and see if you can come up with the fifth term well we have to remind ourselves is for a geometric sequence II for a geometric sequence each successive term is the previous term multiplied by some number and that number we call the common ratio so let's think about it to go from negative 1/32 that's the first term to one eighth what do we have to multiply by what do we have to multiply by let's see we're going to multiply it's going to be multiplied by negative since we went from a negative to a positive so we're going to multiply we're going to multiply by negative and then it's going to be a one over let's see to go from a thirty-two two and eight actually it's not going to be a one over it's going to be this is this is four times as large as that it's going to be negative four negative 132 times negative four is positive one eighth just to just to make that clear negative 1/32 times negative four that's the same thing as times negative four over one it's going to be positive negative times a negative positive positive four over 32 which is equal to 1/8 now let's see if that holds up so to go from 1/8 to negative 1/2 we once again would multiply by negative four negative four times 1/8 is negative four 8 which is negative one half and so then we multiply by negative four again so let me make it clear we're multiplying by negative four each time you multiply by negative four again you get two positive 2 because negative four negative negative four over negative two you can view it that way is positive two and so to get the fifth term in the sequence we would multiply by negative four again and so 2 times negative 4 is negative eight negative 4 is the common ratio for this geometric sequence but just to answer the question what is the fifth term it is going to be negative eight