Question

An arithmetic sequence is defined by the general term tn = -5 + (n - 1)78, where n ∈N and n ≥ 1. What is the recursive formula of the sequence?

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Answer 1

`\text{The general term of an arithmetic sequence:}\ a_n=a_1+(n-1)d\\\\a_n-n-th\ term\\a_1-first\ term\\d-common\ difference\\\\\text{We have}\ t_n=-5+(n-1)78.\ \text{Therefore}\ t_1=-5\ \text{and}\ d=78\\\\\text{The recursive formula of the sequence:}\\\\\left\{\begin{array}{ccc}t_1=-5\\t_n=t_(n-1)+78\end{array}\right`