In Exercises 63–64, find a2 and a3 for each geometric sequence.

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Question

In Exercises 63–64, find a2 and a3 for each geometric sequence.

2, a2, a3, - 54

Accepted Answer

hey everyone here we are asked to determine the missing terms in the given geometric sequence. Now, our first step here before we can begin solving, we need to recall the formula for the general term of a geometric sequence which is a sub N is equal to a sub one times R. To the power of n minus one. And in this formula a sub one is the first term. So we can go ahead and identify our a sub one in reference to our given sequence. So we can look at our first term which we see is 81. So we know that our a sub one is equal to 81. And now we can use our last piece of given information this negative 24 so that we can solve for R. So using this information we see that the fourth term is negative 24. Therefore we know that a sub four is equal to negative 24. And now we can again use this information we've identified and plug it into our formula to solve for R. So instead of a sub N will have a sub four which we see is the value negative 24. So we have negative 24 is equal to a sub one which we identified as 81 times our. And in our formula R is to the power of n minus one. But and in this case is the subscript which we have as four. So we'll have our to the power of four instead of n minus one. And now we can just simplify and solve for R. So dividing both sides by 81. To get our alone. We see that R cubed is equal to 81 divided by negative 24. And now taking the third root of both sides, we see that R. Is equal to negative two thirds. And now with this we can find our missing terms so we can move on to a sub two. So a sub two is equal to a sub one which again is 81 times are which is again we found to be negative two thirds to the power of two because that is our subscript so and is replaced with two minus one. And now simplifying we see that a sub two is equal to -54 and now we can just repeat this to find our last missing term which is a sub three and now a sub three is equal to a sub one which is again 81 times R. Which is negative two thirds to the power of three minus one. And finally simplifying, we see that a sub three is equal to 36. And with this we have identified our two missing terms in our geometric series and we are left with answer choice d. Thanks for watching. I hope you found this video helpful. And I'll see you again next time

In Exercises 63–64, find a2 and a3 for each geometric sequence. 2, a2, a3, - 54

Key Concepts

Geometric Sequence

Common Ratio

Finding Terms in a Sequence

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