1. The following arrays are all composed of three numbers, they are:
$$
\begin{array}{l}
(1,2,3),(2,4,6),(3,8,11), \\
(4,16,20),(5,32,37), \cdots . \\
\left(a_{n}, b_{n}, c_{n}\right) .
\end{array}
$$

Please write an expression for $a_{n}, b_{n}, c_{n}$
$$
a_{n}=
$$
,$b_{n}=$ $\qquad$ ,$c_{n}=$ $\qquad$
2. $a_{n}=n, b_{n}=2^{n}, c_{n}=n+2^{n}$.
From $1,2,3,4,5, \cdots$ conjecture $a_{n}=n$;
From $2,4,8,16,32, \cdots$ conjecture $b_{n}=2^{n}$;
From each set of numbers being “the sum of the first two equals the third” conjecture $c_{n}=n+2^{n}$.