In the sequence 21,700, 23,172, 24,644, 26,116,... which term is ...

Question

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

Accepted Answer

Everyone in this problem. We are given a number sequence and were asked which term is 106,829. The sequence were given as 17,890. 23,628. 26,497. Okay. So let's start and consider what A general arithmetic sequence would look like arithmetic sequence. We would have A N. Is equal to a one plus n minus one times D. Now a one represents the first room And D represents the difference. Okay well we know the first term a one that's gonna be 17,890 as we were given in the problem. But what about d we're gonna leave this as D for now. Well this is gonna be the difference between consecutive terms. Okay so we want to find the difference between the first two terms 2nd and 3rd. Okay if this is an arithmetic sequence the difference d is going to be the same between every single one of them. Okay. And so let's just take the difference here. So if we take 26,497 and we subtract 23,628 we're going to get 2869. Let's just double check that this is an arithmetic sequence and that difference is the same. Let's do the same for the other terms and we're gonna subtract the term proceeding it That's gonna be 20,759. And this is gonna give us 2,869 as well. Okay. And one more. Let's just double check again that the difference between the second term and the first term Is equal and it does indeed. 20,759 -17890 gives us 20 or sorry 2,869. Okay So the difference d. Is equal in these so we do have an arithmetic sequence and we know that the difference is 2869. So our general sequence we can write us A. M. Is equal to 17,890 plus and minus one times the difference. 2869. Okay. We want to find out which term. It's 106829. Okay so we want the term to be 106829 And we know that this is going to be equal to 17,890 plus the term and -1 times the difference. 2869. And we want to find end. What is that term subtracting? 17,890. We're going to get 88,000 Is equal to N -1 times 28,000 sorry 22869 We can divide to get 31 is equal to N -1. And adding gives us N is equal to 32. Okay? So we figured out that this sequence is arithmetic. We've written the equation and we found that the term we're looking for is the 32nd term. Okay. And so the answer here is going to be a the 32nd term. Thanks everyone for watching. I hope this video helped see you in the next one.

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In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?