Answer
The first six terms of the arithmetic sequence are\[1,-4\text{,}-9,-14,-19\text{ and }-2\text{4}\].
Work Step by Step
For the second termn = 2:
\[\begin{align}
& {{a}_{2}}={{a}_{1}}+\left( n-1 \right)d \\
& =1+\left( 2-1 \right)\left( -5 \right) \\
& =1+1\left( -5 \right) \\
& =-4
\end{align}\]
For the third term n = 3:
\[\begin{align}
& {{a}_{3}}={{a}_{1}}+\left( n-1 \right)d \\
& =1+\left( 3-1 \right)\left( -5 \right) \\
& =1+2\left( -5 \right) \\
& =-9
\end{align}\]
For the fourth term n = 4:
\[\begin{align}
& {{a}_{4}}={{a}_{1}}+\left( n-1 \right)d \\
& =1+\left( 4-1 \right)\left( -5 \right) \\
& =1+3\left( -5 \right) \\
& =-14
\end{align}\]
For the fifth term n = 5:
\[\begin{align}
& {{a}_{5}}={{a}_{1}}+\left( n-1 \right)d \\
& =1+\left( 5-1 \right)\left( -5 \right) \\
& =1+4\left( -5 \right) \\
& =-19
\end{align}\]
For the sixth term n = 6:
\[\begin{align}
& {{a}_{6}}={{a}_{1}}+\left( n-1 \right)d \\
& =1+\left( 6-1 \right)\left( -5 \right) \\
& =1+5\left( -5 \right) \\
& =-24
\end{align}\]
Hence, the first six terms of the arithmetic sequence are\[1,-4\text{,}-9,-14,-19\text{ and }-2\text{4}\].
