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![Complete the recursive formula of the arithmetic sequence
{:[0","11","22","33","dots.],[c(1)=◻],[c(n)=c(n-1)+]:}](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/Algebra-1/Sequences/Constructing%20arithmetic%20sequences/Q-2.png)
Complete the recursive formula of the arithmetic sequence ..
Full solution
Q. Complete the recursive formula of the arithmetic sequence ..
- Identify first term and common difference: Identify the first term of the sequence and the common difference between consecutive terms. The first term is , and by observing the sequence, we can see that each term increases by from the previous term. Therefore, the common difference is .
- Write initial condition: Write the initial condition for the recursive formula. The initial condition specifies the first term of the sequence, which is . So, we have .
- Determine recursive part: Determine the recursive part of the formula. Since the common difference is , the recursive part of the formula will add to the previous term. This can be written as for n > 1.
- Combine initial condition and recursive part: Combine the initial condition and the recursive part to write the complete recursive formula for the sequence. The complete recursive formula is:, for n > 1.
