# Video: Finding the General Term of a Given Geometric Sequence

Find, in terms of π, the general term of the geometric sequence β76, β38, β19, β19/2, ...

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### Video Transcript

Find in terms of π the general term of the geometric sequence negative 76, negative 38, negative 19, and negative nineteen halves.

Remember that the formula for the πth term of the geometric sequence is π sub π equals π times π to the π minus one, where π is the first term and π is the common ratio. For the series, we have been given that π is negative 76 because itβs the first term and we can calculate the common ratio, but by dividing the first two terms.

So to find that common ratio again, letβs divide our terms. So letβs take the second term and divide it by the first term. So negative 38 divided by negative 76 reduces to positive one-half. So that means the common ratio that we will be multiplying each number to get the next term would be one-half.

So letβs think about it. Negative 76 times one-half would be negative 38. And then negative 38 times one-half equals negative 19. And negative 19 times one-half is equal to negative nineteen halves. Substituting these values into the equation that we wrote will give us- and the πth term would be represented by π sub π equals negative 76 times one-half to the π minus one power.