Write a rule for the \( n \)th term of the sequence. Then find \( a_{20} \). \( 7,12,17,22, \ldots \) \( a_{n}=\square \) \( a_{20}=\square \)

1. The sequence is \( 7,\,12,\,17,\,22,\,\ldots \). Notice that each term increases by a constant difference: \[ 12-7=5,\quad 17-12=5,\quad 22-17=5. \] 2. Since the difference is constant, this is an arithmetic sequence with first term \( a_1 = 7 \) and common difference \( d = 5 \). 3. The formula for the \( n \)th term of an arithmetic sequence is: \[ a_n = a_1 + (n-1)d. \] 4. Substitute \( a_1 = 7 \) and \( d = 5 \) into the formula: \[ a_n = 7 + (n-1) \cdot 5. \] 5. Simplify the formula: \[ a_n = 7 + 5n - 5 = 5n + 2. \] 6. Now, to find \( a_{20} \), substitute \( n=20 \) into the formula: \[ a_{20} = 5(20) + 2 = 100 + 2 = 102. \] \( a_{n}=5n+2 \) \( a_{20}=102 \)