Write the first five terms of the sequence whose first term is 9 ...

Question

Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n-1 is even, a_n=3a_n-1 + 5 if a_n-1 is odd for n≥2.

Accepted Answer

Hello, today we're going to be fighting the first six terms of a given sequence. So what we are told is that any term in the sequence is equal to two times the previous term plus three, if the previous term is even, or any term is equal to the previous term squared minus one, if the previous term is odd. So in order to find the first six terms, we need to first figure out what our first term of the sequence is going to be. Well, we are given the statement that N has to be greater than or equal to two. With that being said, we can allow our first term a sub one to equal to two because two is going to be the minimum allowed value for any given value of N. So we're gonna use this to help us find the remaining five terms. Now, when we're trying to look for a sub two, which is going to be the second term in the sequence, we need to first figure out which one of these conditions were going to be using. Well, keep in mind that if the previous term is even, we use this statement or if the previous term is odd, we use this statement, the previous turn to a sub two is going to be a sub one and a sub one is equal to two, which is an even number. So that means we're going to be using the statement two times the previous term plus three to figure out what a time a sub two is because the previous term is even. So taking two and plugging this into the statement is going to give us two times two because the previous term is one plus three, simplifying this two times two is going to give us four and four plus three is going to give us seven. So a sub two is going to equal to seven. Now, if we want to find a sub three, we have to take a look at what the previous term is. While we know that a sub two came out of seven, which is going to be an odd number. And since seven is an odd number, in order to find a sub three, we're going to be plugging in a sub two into the bottom statement here. So when we find a sub three, we're going to take seven square it and minus one seven squared is going to give us 49 minus one is going to give us 48. And now we're going to use this term to help us find a sub four, which is the fourth term, Now repeating this pattern 48, which is the previous term is an even number. And since we know it's an even number, we're going to be using the first statement of the given sequence. So that's going to give us two times 48 plus three. For the fourth term, 48 times two is going to give us 96 96 plus three is going to simplify to give us 99. And now for the fifth term, 99 is an odd number, which means we're going to use the bottom statement to find a sub five. That's going to give us 99 squared minus 99 squared is going to give us 9801. And that value minus one is going to leave us with 9800. Finally, we're going to look for our sixth term, which is a sub six and 98,000 is an even number. So we're going to be using the first statement in our given sequence to find our last term that's going to give us two times 9800 plus three, Two times 9800 is going to give us 19, and plus three is going to give us 19,603, which is going to be the last term in the sequence. So now that we have all of our six terms, let's just go ahead and quickly list it out. So listening to the six terms, we ended up with 2748, 9,819,603. This is going to be the first six terms of the given sequence. And with that being said, the answer to this problem is going to be be. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n-1 is even, a_n=3a_n-1 + 5 if a_n-1 is odd for n≥2.

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