Questions: Find an explicit formula for the arithmetic sequence -5, 13, 31, 49, ... Note: the first term should be b(1).

Solution Steps

To find an explicit formula for an arithmetic sequence, we need to identify the first term and the common difference. The first term \( b(1) \) is given as \(-5\). The common difference can be found by subtracting the first term from the second term. Once we have these, the formula for the \( n \)-th term of an arithmetic sequence is given by \( b(n) = b(1) + (n-1) \times \text{common difference} \).

The first term of the arithmetic sequence is given as \( b(1) = -5 \).

The common difference \( d \) of an arithmetic sequence is calculated by subtracting the first term from the second term: \[ d = 13 - (-5) = 18 \]

The formula for the \( n \)-th term of an arithmetic sequence is given by: \[ b(n) = b(1) + (n-1) \times d \] Substituting the known values: \[ b(n) = -5 + (n-1) \times 18 \]

Final Answer