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Write an explicit formula for a_(n), the n^("th ") term of the sequence 9,14,19,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 9,14,19,… 9,14,19, \ldots \newlineAnswer: an= a_{n}=

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Q. Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 9,14,19,… 9,14,19, \ldots \newlineAnswer: an= a_{n}=
  1. Determine Common Difference: To find the explicit formula for the nnth term of the sequence, we first need to determine the common difference between consecutive terms.
  2. Calculate Common Difference: We subtract the first term from the second term to find the common difference. 14−9=514 - 9 = 5
  3. Identify Arithmetic Sequence: The common difference is 55. This means that each term is 55 more than the previous term. The sequence is an arithmetic sequence.
  4. Arithmetic Sequence Formula: The explicit formula for an arithmetic sequence is given by:\newlinean=a1+(n−1)da_n = a_1 + (n - 1)d\newlinewhere a1a_1 is the first term and dd is the common difference.
  5. Substitute Values: We know that a1=9a_1 = 9 and d=5d = 5. Let's substitute these values into the formula.\newlinean=9+(n−1)×5a_n = 9 + (n - 1) \times 5
  6. Distribute and Simplify: Simplify the formula by distributing the 55 into the parentheses.an=9+5n−5a_n = 9 + 5n - 5
  7. Combine Like Terms: Combine like terms to get the final explicit formula. an=5n+4a_n = 5n + 4

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