Question

- What is the closed linear form of the sequence 3, 4,5, 6, 7, ...?

Answer 1

`\begin{gathered} Sequence\text{ general equation} \\ a_n=a_1+(n-1)d \\ \text{From given information} \\ a_1=3 \\ \text{From the general equation} \\ a_n=a_1+(n-1)d \\ a_n-a_1=(n-1)d \\ d=(a_n-a_1)/(n-1) \\ \text{Choosing second term, n=2, a}_2=4 \\ d=(4-3)/(2-1) \\ d=1 \\ \text{Hence The closed linear form of the sequence is} \\ a_n=3_{}+(n-1)\cdot1 \\ a_n=3_{}+(n-1) \\ a_n=3_{}+n-1 \\ a_n=3_{}-1+n \\ a_n=2+n \end{gathered}`