Exercises 88–90 will help you prepare for the material covered in...

Question

Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −2, 4, −8, 16, ………. Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?

Accepted Answer

Hey everyone here we are asked to evaluate each of these ratios for the following sequence. With the values -27, 81, -243 and 729. So now we can begin here by identifying each of the values in our sequence. So beginning with a sub one, A sub one represents our first term. So our first term in our sequence is nine. And now for a sub two we have the subscript two which tells us we are looking for the second term which in this case is negative 27. Next for a sub three we look again at our sequence and see that our third term here is 81. And then for a sub four, our 4th term is -243. And finally for a sub five, our fifth term leaves us with the last term in the given sequence which is the value 729. So now since we have identified each of our terms here we can go ahead and evaluate the ratios. So first we have a sub two divided by a sub one. So again these values for the numerator we have negative 27 for the denominator we have nine negative 27 divided by nine gives us negative three. Then we can move on to our second ratio. We have a sub three divided by a sub two. And then again for our numerator, our third turn was 81 for the denominator, a sub two was negative 27. And now simplifying this fraction here we end up again with negative three. And now we can move on to the fourth ratio where we have a sub four divided by a sub three with our numerator. Our fourth term was negative 243. Then for the denominator our value is 81. Simplifying this ratio we get the ratio of negative three and now we can move on to our final ratio. Where we have a sub five divided by a sub four. Beginning with our numerator we have the value 729. For our denominator we have negative 243. Now simplifying, we see that we have a ratio here also of -3. So now we have found the ratio for each of the unknowns here and this tells us that the ratio of the term to the ratio that comes before it is always negative three. And with this we are left with answer choice C. Thanks for watching. I hope you found this video helpful and I'll see you again next time

Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −2, 4, −8, 16, ………. Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?

Key Concepts

Sequences

Ratios of Terms

Observational Analysis

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