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Find an explicit formula for the arithmetic sequence -11,-3,5,13,dots Note: the first term should be b(1). b(n) = ◻

Find an explicit formula for the arithmetic sequence −11,−3,5,13,… -11,-3,5,13, \ldots \newlineNote: the first term should be b(1) b(1) .\newlineb(n)=□b(n) = \square

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Q. Find an explicit formula for the arithmetic sequence −11,−3,5,13,… -11,-3,5,13, \ldots \newlineNote: the first term should be b(1) b(1) .\newlineb(n)=□b(n) = \square
  1. Identify Sequence Type: Identify the type of sequence. The sequence −11,−3,5,13,…-11, -3, 5, 13, \ldots has a common difference between consecutive terms, indicating that it is an arithmetic sequence.
  2. Calculate Common Difference: Calculate the common difference dd of the sequence. To find the common difference, subtract the first term from the second term: d=−3−(−11)=−3+11=8d = -3 - (-11) = -3 + 11 = 8.
  3. Use Explicit Formula: Use the explicit formula for an arithmetic sequence, which is b(n)=b(1)+(n−1)db(n) = b(1) + (n-1)d, where b(1)b(1) is the first term and dd is the common difference. For this sequence, the first term, b(1)b(1), is −11-11 and the common difference, dd, is 88.
  4. Substitute Values: Substitute the values of b(1)b(1) and dd into the formula to write an expression to describe the sequence. The expression for the sequence is b(n)=−11+(n−1)×8b(n) = -11 + (n-1) \times 8.
  5. Simplify Expression: Simplify the expression. b(n)=−11+8n−8b(n) = -11 + 8n - 8, which simplifies to b(n)=8n−19b(n) = 8n - 19.

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