Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

6, 7, 8, 9, ...

Answer 1

Explanation:

`a_1=6\\a_2=a_1+1\to a_2=6+1=7\\a_3=a_2+1\to a_3=7+1=8\\a_4=a_3+1\to a_4=8+1=9\\\vdots\\\\\text{The recursive formula}\\a_n=\left\{\begin{array}{ccc}a_1=6\\a_n=a_(n-1)+1\end{array}\right\\\\\text{It's an arithmetic sequence with}\ a_1=6\ \text{and difference}\ d=1\\\\\text{The explicit formula of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=6+(n-1)(1)\\a_n=6+n-1\\a_n=5+n\\\\a_n=n+5`