Using explicit formulas of geometric sequences | Mathematics I | High School Math | Khan Academy

The geometric sequence Asobi is defined by the formula, and so they say they tell us that the E term is going to be equal to 3 * -1/4 to the IUS 1 power.

So, given that, what is a sub5, the fifth term in the sequence?

So pause the video and try to figure out what is a subscript 5.

All right, well we can just use this formula. A sub five is going to be every time where I see an I, I replace it with a five.

Is going to be equal to 3 * -1/4 to the 5 - 1 power.

Well, that's equal to 3 * -1/4 to the 4th 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 3 * let's see, 1 to the 1/4 is 1.

The 4th power is just 1, and then 4 to the 4th power, let's see, 4 * 4 is 16.

So 4 * 4 is 4 * 4, so 16 * 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 3 over 256.