Use the formula for the general term (the nth term) of a geometri...

Question

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a(sub 6) when a(sub 1) = 16, r = 1/2

Accepted Answer

Welcome back. I'm so glad you're here. We've got a geometric sequence with some givens and we want to find a sub seven or the value of the seventh term in our geometric sequence. So we're looking for a sub seven. And what do we know? We know that the value of the first term or a sub one is 245. We know that our ratio are is 1/ and we know that our N the number of that term we're looking for is value The N is seven. And when we are looking for the value of an term, We recall from previous lessons that we've got a formula for that. The formula is a sub one times are raised to the N -1 -1 And we know all of these things. We can fill them in a sub one is 245 Times are which is 1 5th And that is raised to the end or the 7 -1? Do some simplifying? Got 245 times. 1/5 raised to the seven minus one which is 6, 245 times. Well, one race to the sixth is one and five raised to the sixth is 15,625. Now, multiplying straight across, we've got 245 divided by 15,625. Looking at all of our answer choices, they're looking for a reduced fraction as an answer, not for a decimal. So what can we divide these both by well we can divide them both by five. They both end with five, So 245 divided by five is And 15,625 divided by five is 3,125. We can check with the calculator, but the only factors of 49 are seven and 49 and none of those going to 3,125. So we know that that is as reduced as it's going to get and that matches with answer choice a while done, we'll catch you on the next one.

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