Question

write a formula for the general term (the nth term) of the arithmetic sequence shown below. do not use a recursion formula. then use the formula for ( a_n ) to find ( a_{20} ), the 20th term of the sequence. ( a_n = a_{n - 1} - 17, a_1 = 29 ) ( a_n = 46 - 17n ) ( a_{20} = square ) (simplify your answer.)

Explanation:

Step1: Identify the formula for \(a_n\)

We are given the general term formula \(a_n = 46 - 17n\).

Step2: Substitute \(n = 20\) into the formula

To find \(a_{20}\), we substitute \(n = 20\) into \(a_n = 46 - 17n\). So we have \(a_{20}=46 - 17\times20\).

Step3: Calculate the value

First, calculate \(17\times20 = 340\). Then, \(46-340=-294\).

Answer:

\(-294\)