Write a rule for the \( n \)th term of the sequence. Then find \( a_{2} \) \( 11.7,10.8,9.9,9, \ldots \) \( a_{n}=\square \) \( a_{20}=\square \)

- The sequence is arithmetic because each term decreases by the same constant. - The first term is \[ a_1 = 11.7 \] - The common difference is \[ d = 10.8 - 11.7 = -0.9. \] - The general formula for the \( n \)th term of an arithmetic sequence is \[ a_n = a_1 + (n-1)d. \] - Substituting the values, we get \[ a_n = 11.7 + (n-1)(-0.9) = 11.7 - 0.9(n-1). \] - To find \( a_{2} \), substitute \( n = 2 \): \[ a_{2} = 11.7 - 0.9(2-1) = 11.7 - 0.9 = 10.8. \] - To find \( a_{20} \), substitute \( n = 20 \): \[ a_{20} = 11.7 - 0.9(20-1) = 11.7 - 0.9(19) = 11.7 - 17.1 = -5.4. \] Thus, \[ a_n = 11.7 - 0.9(n-1) \] \[ a_{2} = 10.8 \] \[ a_{20} = -5.4 \]