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Write an explicit formula for a_(n), the n^("th ") term of the sequence 25,15,5,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 25,15,5,… 25,15,5, \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 25,15,5,… 25,15,5, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Arithmetic Sequence: The given sequence is 25,15,5,…25, 15, 5, \ldots which is an arithmetic sequence because the difference between consecutive terms is constant.
  2. Find Common Difference: To find the common difference dd, subtract the second term from the first term: d=15−25=−10d = 15 - 25 = -10.
  3. Use Arithmetic Sequence Formula: The first term of the sequence a1a_1 is 2525. The nnth term of an arithmetic sequence is given by the formula an=a1+(n−1)da_n = a_1 + (n - 1)d.
  4. Substitute Values: Substitute the values of a1a_1 and dd into the formula: an=25+(n−1)(−10)a_n = 25 + (n - 1)(-10).
  5. Simplify Formula: Simplify the formula: an=25−10n+10a_n = 25 - 10n + 10.
  6. Final Explicit Formula: Combine like terms to get the final explicit formula: an=35−10na_n = 35 - 10n.

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