Video: Finding the General Term of a Given Geometric Sequence

Video Transcript

Find in terms of 𝑛 the general term of the geometric sequence negative 76, negative 38, negative 19, and negative nineteen halves.

Remember that the formula for the 𝑛th term of the geometric sequence is 𝑇 sub 𝑛 equals 𝑎 times 𝑟 to the 𝑛 minus one, where 𝑎 is the first term and 𝑟 is the common ratio. For the series, we have been given that 𝑎 is negative 76 because it’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, let’s divide our terms. So let’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 let’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 𝑛th term would be represented by 𝑇 sub 𝑛 equals negative 76 times one-half to the 𝑛 minus one power.