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Arithmetic sequence equation1/29/2024 ![]() ![]() Well now that we know thatĪ-sub-3 is negative 11, so this is negative 11, we could figure out a-sub-4 is negative 11 minus 2, which is equal to negative 13. ![]() Well that starts helping us out because if a-sub-2 is negative 9, if this is negative 9, then a-sub-3 is negative 9 minus 2, which is equal to negative 11. A-sub-1 is negative 7, so if this is negative 7, then a-sub-2 is negative 7 minus 2, which is equal to negative 9. We still don't know what a-sub-2 is, and so, we could write, a-sub-2 is equal to a-sub-2 minus 1, so that's a-sub-1 minus 2. A-sub-3 is going to be equal to a-sub-3 minus 1, so a-sub-2 minus 2. So we could say that a-sub-4 is equal to, well if we use the second line again, it's going to be a-sub-3, minus 2. Well, we don't know whatĪ-sub-4 is just yet, so let's try to figure that out. Let's see what we can make of this, so a-sub-5, a-sub-5 is going to be equal to, we'll use this second line right here, a-sub-5 is going to be equal to a-sub-4 minus 2. Recursive definition of our arithmetic sequence. To be a-sub-i minus 1 minus 2, so this is actually a It in terms of the previous terms, so a-sub-i is going The arithmetic sequence a-sub-i is defined by the formula a-sub-1, they gave us the first term, and they say, every other term, so a-sub-i, they're defining ![]() This arithmetic sequence is going to be 61. This is 57, and 4 plus 57 is equal to 61, so the 20th term in 3 times 19, let's see, 3 times 19 is 57, right? It's 30 plus 27, yep. This is going to be equal to 4 plus 3 times 20 minus 1 is 19. Wherever we saw an i, we put a 20, and now we can just compute We would put a 20 in, so it's going to be 4 plus 3 times 20 minus 1, so once again, just to be clear, a-sub-20, where instead of a-sub-i, A-sub-20, we just use thisĭefinition of the ith term. What is a-sub-20? And so a-sub-20 is theĢ0th term in the sequence and I encourage you to pause the video and figure out what is the 20th term? Well, we can just thinkĪbout it like this. The ith term in the sequence is going to be 4 plus 3 times i minus 1. All right, we're told that theĪrithmetic sequence a-sub-i is defined by the formula where ![]()
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