## Thinking Mathematically (6th Edition)

The ${{n}^{th}}$term of given arithmetic sequence is${{a}_{n}}=200+(n-1)(-20)$. The twentieth term of the arithmetic sequence is$-180$.
Hence, the general term for the given arithmetic sequence is \begin{align} & {{a}_{n}}={{a}_{1}}+\left( n-1 \right)d \\ & \,\,\,\,\,\,=200+(n-1)(-20) \\ \end{align} To find the twentieth term put $n=20$ in the above formula, to get \begin{align} & {{a}_{20}}={{a}_{1}}+\left( 20-1 \right)d \\ & =200+19\cdot \left( -20 \right) \\ & =200-380 \\ & =-180 \end{align} The ${{n}^{th}}$term of given arithmetic sequence is${{a}_{n}}=200+(n-1)(-20)$. The twentieth term of the arithmetic sequence is$-180$.