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Complete the recursive formula of the arithmetic sequence \newline20,26,32,38,20,26,32,38,\dots \newlinea(1)=a(1)=\square\newlinea(n)=a(n1)+6a(n) = a(n-1) +6

Full solution

Q. Complete the recursive formula of the arithmetic sequence \newline20,26,32,38,20,26,32,38,\dots \newlinea(1)=a(1)=\square\newlinea(n)=a(n1)+6a(n) = a(n-1) +6
  1. Determine Common Difference: To find the recursive formula for the arithmetic sequence, we first need to determine the common difference between consecutive terms.\newlineWe can subtract the first term from the second term to find this common difference.\newline2620=626 - 20 = 6
  2. Write Recursive Formula: Now that we know the common difference is 66, we can write the recursive formula. The first term a(1)a(1) is given as 2020.\newlineSo, a(1)=20a(1) = 20.
  3. Finalize Recursive Formula: The recursive formula will then be a(n)=a(n1)+6a(n) = a(n-1) + 6 for n > 1, where a(n)a(n) is the nnth term and a(n1)a(n-1) is the (n1)(n-1)th term.

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