Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the 30 th 30^{\th} term. { − 9 , − 4 , 1 , 6 , … } \left\lbrace-9,-4,1,6,\ldots\right\rbrace { − 9 , − 4 , 1 , 6 , … }

Alright, everyone. So in this practice problem, we're gonna find the general formula for this arithmetic sequence that's given to us. And without using a recursive formula, we're gonna use this general formula, calculate the 30th term in the sequence. So let's go ahead and get started. Remember that an arithmetic sequence is, again, one where the difference between the numbers is the same. And in order to calculate a general formula, not a recursive formula, we're gonna use this formula over here, where all we need is we need the the first term in the sequence, and we need the common difference, And that'll allow us to calculate any term in the sequence without having to know the previous one. So for example, in this arithmetic sequence here, we have we have negative 9, negative 4, 1, and 6. The first term in the sequence, a 1, is equal to negative 9. And now let's look at the common difference between the numbers. We have negative 9, negative 4, in other words, you have to add 5, negative 4 to positive 1, add 5, 1 to 6, add 5. So, therefore, the difference, the common difference that lowercase d is just equal to 5. So we can use both of these numbers that a one is negative 9 and d is negative 5 to write our general formula. That's all we need. And what would this what this general formula is, it's just gonna be a n equals a 1 plus d and then parenthesis n minus 1. Alright? So in other words, the a nth term, the nth term is just gonna be the negative 9 that we have from the first term, plus the common difference of 5 times n minus 1. Remember, the n minus one comes from the fact that you're already accounting for the 1st term, so you almost like to you know, so you're sort of knocked down the index by 1, and that's just gonna be a multiple of, the common difference. That's how you calculate any nth term. Alright? So this is the general formula for your arithmetic sequence. You can calculate any term based on this formula. In fact, you could even go and calculate the first four terms, and you would find that you would actually get those numbers here. Alright? So then how do we calculate now the 30th term? Well, we basically just plug in n equals 30 into our formula over here. So the 30th term is really just gonna be negative 9 plus the common difference 5 times 30 minus 1. In other words, it's gonna be negative 9 plus 5 times 29. And if you go ahead and punch this into your calculator, what you're gonna see is that the 30th term is equal to a 136. So the a 30 is gonna be a 136. So how that was much faster than if you actually had to write out 30 terms. But if you did, you would still find that it would be a 136. Alright? So So hopefully, you got that right. Let me know if you have any questions. Thank you for watching.

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Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the 30th30^{\(\th\)} term.{−9,−4,1,6,…}\(\left\)\(\lbrace\)-9,-4,1,6,\(\ldots\[\right\]\rbrace\){−9,−4,1,6,…}

다음 시청

Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30 raised to the th power$ term.
$\left\)\(\lbrace\)-9,-4,1,6,\(\ldots\[\right\]\rbrace$