The sequences in Exercises 13–18 are defined using recursion form...

Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=4 and a_n=2a_n-1 + 3 for n≥2

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to write the first four terms of a sequence that uses a record in formula and in this case we're given a one is equal to eight and the sequence pattern or a N. Is equal to six times a N - Plus 1. 4 and greater than or equal to two. So because we want to find the first four terms we need to find where n equals one Through an equals four. So when N is equal to one we're actually given a one equals eight. So we're already given the first value, the first value is eight. So we can go ahead and go where N is equal to two. And that's where this record asian formula comes into play because now we have an equal Or greater than two. So we can use the equation A two is equal to six times a 2 -1 Plus one. So if I start simplifying I see that the second term a two is equal to six times a one plus one. And we know the value of a one A one is 8. So I can plug that in. So a two is equal to six times eight plus one. So six times 8 is 48 plus one. So my second term is 49. And we can continue if we look at the third term where N is equal to three we're gonna use that same formula but now I have a three is equal to six Times A 3 - Plus one. So now I have a three is equal to six A two plus one. And we know the value of a two since we solved for it. So this becomes six times 49 plus one, so six times 49 is 2 plus one, so a three is equal to 295. And finally solving for our fourth term where n is equal to four, we have a four or the fourth term in the A sequence Is equal to six times a 4 -1 plus one. So this is six times a three plus one. And we just solved for a three, it's 2 95. So this is equal to six times 2 95 plus one and six times 2 95 is plus one. So a four is equal to 1,771. And here you can see that now we have the values of the first four terms in the sequence. So I'm going to pull those out. It's 8: 295 and 1771. So this becomes my final answer for the first four terms and you can see that this aligns with answer choice D. So hopefully this video helped and see you next time

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The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=4 and a_n=2a_n-1 + 3 for n≥2

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