About this video
The geometric sequence a_i = 3 x (-1/4)^(i-1) is used to find the fifth term. Substituting i = 5 gives 3 x (-1/4)^4; an even power of a negative is positive, and 4^4 = 256, so a_5 = 3/256.
You'll be able to
- substitute into an explicit geometric formula to find a term.
- explain why a negative number raised to an even power is positive.
Key words
- geometric sequence
- A sequence where each term is multiplied by the same number to get the next.
- explicit formula
- A formula that gives any term directly from its position i.
- even power
- An exponent like 2 or 4; a negative number to an even power is positive.
Transcript
- [Voiceover] The geometric sequence A sub I is defined by the formula and so they tell us that the Ith term is going to be equal to three times negative one fourth 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?
Alright, well, we can just use this formula. A... A sub five is going to be... is everywhere I see an I or a place 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... lets see, we're raising it to an even power so it's going to give us a positive value since we're gonna be multiplying the negative an even number of times so it's gonna be a positive value so it's gonna be three times... let's see, one to the one fourth is- oh, one to the fourth power is just one, and then four to the fourth power...
let's see, four squared is 16, so four squared times four squared is four 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 four 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.
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