Problem Solving (PS) | If a sequence is given by the expression S_n = S_{n-1} + 3 and S_1 = 1

\(S_n = S_{n-1} + 3\) and
\(S_1=1\)

\(S_2 = S_{n-1} + 3\)

\(S_2 = S_{1} + 3\) =4
\(S_3 = S_{2} + 3\) = 7

OR
\(S_1 = 1\)\(S_2 = 1 + 3\)
\(S_3 = 1 + 3 + 3\)\(S_4 = 1 + 3 + 3 + 3\)

For\(S_{n}\) , then, the first term is\(S_1 = 1\) , and the number of 3s is one fewer than\(n\) . It's an arithmetic series, first term is 1, common difference of 3, such that

\(S_n = S_1 + 3(n-1)\)
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