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Write an explicit formula that represents the sequence defined by the following recursive formula: a_(1)=-10" and "a_(n)=a_(n-1)+6 Answer: a_(n)=

Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=−10 and an=an−1+6 a_{1}=-10 \text { and } a_{n}=a_{n-1}+6 \newlineAnswer: an= a_{n}=

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Q. Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=−10 and an=an−1+6 a_{1}=-10 \text { and } a_{n}=a_{n-1}+6 \newlineAnswer: an= a_{n}=
  1. Identify First Term: Identify the first term of the sequence.\newlineThe first term is given as a1=−10a_{1} = -10.
  2. Identify Common Difference: Identify the common difference in the recursive formula.\newlineThe recursive formula an=an−1+6a_n = a_{n-1} + 6 suggests that the common difference between consecutive terms is 66.
  3. Write Explicit Formula: Write the explicit formula based on the first term and the common difference.\newlineThe explicit formula for an arithmetic sequence is given by an=a1+(n−1)da_n = a_1 + (n - 1)d, where a1a_1 is the first term and dd is the common difference.
  4. Substitute Known Values: Substitute the known values into the explicit formula.\newlineSubstituting a1=−10a_{1} = -10 and d=6d = 6 into the formula, we get an=−10+(n−1)×6a_{n} = -10 + (n - 1) \times 6.
  5. Simplify Formula: Simplify the explicit formula.\newlineSimplifying the formula, we get an=−10+6n−6a_{n} = -10 + 6n - 6.\newlineCombining like terms, we get an=6n−16a_{n} = 6n - 16.

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