Q. Find an explicit formula for the arithmetic sequence−11,−3,5,13,…. Note: the first term should be b(1).b(n)=□
Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence −11, −3, 5, 13, ... has a common difference between consecutive terms, so it is an arithmetic sequence.
Find common difference: Determine the common difference d of the sequence by subtracting any term from the term that follows it. For example, the difference between the second term −3 and the first term −11 is −3−(−11)=8.
Use explicit formula: Use the explicit formula for an arithmetic sequence, b(n)=b(1)+(n−1)d, where b(1) is the first term and d is the common difference. For this sequence, the first term, b(1), is −11 and the common difference, d, is 8.
Write expression for sequence: Substitute the values of b(1) and d into the formula to write an expression to describe the sequence. The expression for the sequence −11,−3,5,13,extellipsis is b(n)=−11+(n−1)imes8.
Simplify expression: Simplify the expression to find the explicit formula. b(n)=−11+8n−8, which simplifies to b(n)=8n−19.
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