This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the number of terms in the arithmetic sequence, we use the formula for the n^th term of an arithmetic sequence. Given the sequence: 7, 10, 13, ..., 55 Step 1: Identify the first term (a_1). The first term is a_1 = 7. Step 2: Calculate the common difference (d). The common difference is the difference between consecutive terms: d = 10 - 7 = 3 d = 13 - 10 = 3 So, the common difference is d = 3. Step 3: Identify the last term (a_n). The last term given in the sequence is a_n = 55. Step 4: Use the formula for the n^th term of an arithmetic sequence. The formula is: a_n = a_1 + (n-1)d Substitute the known values into the formula: 55 = 7 + (n-1)3 Step 5: Solve the equation for n. First, subtract 7 from both sides: 55 - 7 = (n-1)3 48 = (n-1)3 Next, divide both sides by 3: (48)/(3) = n-1 16 = n-1 Finally, add 1 to both sides to find n: n = 16 + 1 n = 17 The number of terms in the sequence is 17.