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We can find the terms of this sequence easily enough.
\begin{equation*}
3, 8, 14, 24, 33, 33, 45,\ldots\text{.}
\end{equation*}
Here \(b_1\) is just \(a_1\text{,}\) but then
\begin{equation*}
b_2 = 3+5 = a_1 + a_2\text{,}
\end{equation*}
\begin{equation*}
b_3 = 3+5+6 = a_1 + a_2 + a_3\text{,}
\end{equation*}
and so on.
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