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=7 and a_n=a_n-1 + 5 for n≥2

Accepted Answer

everyone in this problem. We are asked to write the first four terms of the sequence. Using the Rikers in formula were given a one is equal to nine and a N is equal to a and minus one plus two. For n bigger than or equal to two. Okay, so the first four terms, we'll start with the first term which is going to be a one and this one were given a one is equal to nine. Alright, We're done with the first term. Now we can do the second term. The second term is going to be a two. Okay, so and it's too so we can use the formula on the right, So we're gonna a two is equal to a 2 - Plus two. Okay. According to our formula, this is going to be equal to a one plus two which is nine plus two which is gonna equal 11. Yes, we have a one, we have a two. Now we need to do a three and a four, so let's go over here, so we can keep everything on the same page. A three. Using our formula is going to be a 3 - plus two. Oh this is gonna be a 2-plus 2 Which is equal to 11-plus 2 which is equal to 13. We're told this is a record Asian formula. And what that means is you're using the previous value to calculate the new value. Okay, so we had to use a to the value of 11 we just found in order to find a three. Okay, so you're kind of building yourself up term by term. Alright. And finally a four according to our formula is a 4 -1 plus two, Just equal to a 3-plus 2 Which is equal to 13-plus 2 Which gives us an a four value of 15. What you'll notice here is that all these terms differ by two? Okay we go 9 11 13 15. And if you look at the formula were given we have a n minus one. So the previous term plus two. Okay, so this is like an arithmetic sequence every term we find by adding two to the previous term. Okay, so too is our common difference and we add that to the previous term to get the new term. Alright so we have 9, 11, 13 and 15 for our first four terms. And so we have answer a that's it for this one. Thanks everyone for watching See you in the next video.

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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=7 and a_n=a_n-1 + 5 for n≥2