(Notice that this equation says, if I want a_4, I take a_3 and multiply by r, which makes sense)įor example, consider the geometric sequence, The value of a_1 and an equation that tells us how to get to the next term. Once again, the recursive formula will consist of two parts. Similarly to the previous example, from this geometric sequence, we need 2 things: If it makes sense, I'll explain geometric sequences. Using the same values from our previous example, The following is the general explicit formula for arithmetic sequences. If we need to find a value further ahead in the sequence, we use the explicit formula. And if I want a_19, I need to find a_18 and so on and so forth. Now, we can see that the first term is 2, so a_1= 2īut notice that the limitation of this approach is that if I want to find a_20, I have to find a_19. We find the common difference by subtracting successive terms and checking that adding this value does get us to the next number in the sequence. (Notice that this equation says, if I want a_4, I take a_3 and add d, which makes sense)įor example, consider the arithmetic sequence, The recursive formula will consist of two parts.
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