Question Video: Finding the Next Three Terms in a Geometric Sequence Mathematics

Find the next 3 terms in the geometric sequence 100, βˆ’10, 1, βˆ’0.1, 0.01, ….

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Video Transcript

Find the next three terms in the geometric sequence 100, negative 10, one, negative 0.1, 0.01, and so on. So we’ve got the first five terms, π‘Ž one, π‘Ž two, π‘Ž three, π‘Ž four, and π‘Ž five. And the first thing I need to do is to work out what the common ratio is. What do I need to multiply π‘Ž one by to get π‘Ž two and so on? And if you remember the way that we do this is we divide one term by its previous term to find out what the ratio is. And looking through there, I reckon the second and third terms are gonna be the easiest ones to divide. And although you get the same answer no matter which consecutive pair you divided, this one’s easy because it’s one divided by negative 10 which is negative a tenth.

So the common ratio is negative a tenth. We need to multiply each term by negative a tenth to get the next term. So to find the next three terms, I just need to take the last term that we had and multiply that by negative a tenth, then multiply that by negative a tenth, and multiply that by negative a tenth. So the sixth term is the fifth term times negative a tenth; that’s, 0.01 times negative a tenth, which is negative 0.01. So multiplying by negative a tenth is the same because it’s dividing by negative 10. So this is relatively easy to do. So the sixth term times negative a tenth, the two negatives are gonna cancel out to make it positive. And 0.001 divided by 10 is 0.0001. And doing the same, the eighth term is negative 0.00001. So we just need to write our answer out there nice and clearly.

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