Question

Find the 4 terms of the sequence given by the recursive definition

Answer 1

`\begin{gathered} \text{Given} \\ a_n=2a_(n-1)-n \\ a_1=3 \end{gathered}`
`\begin{gathered} a_1=3 \\ \; \\ a_2=2a_(2-1)-2 \\ a_2=2a_1-2 \\ a_2=2(3)-2 \\ a_2=6-2 \\ a_2=4 \\ \; \\ a_3=2a_2-3 \\ a_3=2(4)-3 \\ a_3=8-3 \\ a_3=5 \\ \; \\ a_4=2a_3-4 \\ a_4=2(5)-4 \\ a_4=10-4 \\ a_4=6 \end{gathered}`

Therefore, the first 4 terms of the sequence is 3,4,5,6.