The twelfth term of an anithmetic sequence is 5 and the common difference of the sequence is 3 (a) Determine which term has a value of 47

To find which term has a value of 47, we can use the formula for the nth term of an arithmetic sequence, given by \( a_n = a_1 + (n-1)d \). We know the twelfth term (\( a_{12} \)) is 5, which can be expressed as: \[ 5 = a_1 + (12-1) \cdot 3 \] This simplifies to: \[ 5 = a_1 + 33 \] \[ a_1 = 5 - 33 = -28 \] Now, to find which term equals 47, we set \( a_n = 47 \): \[ 47 = -28 + (n-1) \cdot 3 \] \[ 47 + 28 = (n-1) \cdot 3 \] \[ 75 = (n-1) \cdot 3 \] \[ n-1 = 25 \quad \Rightarrow \quad n = 26 \] Thus, the term that has a value of 47 is the 26th term. The answer is: The 26th term of the arithmetic sequence has a value of 47.