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Using explicit formulas of geometric sequences

Video transcript

the geometric sequence a sub is defined by the formula and so they say the tell us that the eighth term is going to be equal to three times negative 1/4 to the I minus one power so given that what is a sub five the fifth term in the sequence so pause the video and try to figure out what is a subscript five all right well we can just use this formula a a sub five is going to be every is everywhere I see and I I replace it with a five is going to be equal to three times negative one fourth to the five minus one power well that's equal to three times negative one fourth to the fourth power well that's going to be equal to let's see we're raising it to an even power so it's going to give us a positive value since we're going to be multiplying the negative an even number of times so it's going to be a positive value so it's going to be three times let's see one to the one-fourth is one to the fourth power is just one and then four to the fourth power let's see 4 squared is 16 so 4 squared times four squared is 4 to the fourth so it's 16 times 16 is 256 256 and once again I know it's going to be positive because I'm multiplying a negative times itself 4 times or I'm multiplying four negatives together so that's going to give me a positive value so I get three over 256 and we're done that's the fifth term in our sequence positive three over 256