## Subject 1

a) The 20th term is 77 .................................................. $1 p$

$S=1+5+9+\ldots+77=780$ $.2 p$

b) The $n$-th term of the sequence is $t_{n}=4(n-1)+1=4 n-3, n \in \mathbf{N}^{*} \ldots . . .1 p$ $t_{2013}=8049$................................................................................... $1 p$

c) We check if the equation $4 n-3=2013$ has solutions in $\mathbf{N}$.......................1p $n=504$, so 2013 is a term of the sequence ......................................... $1 p$
## Subject 1

Consider the sequence: $1,5,9,13, \ldots$.

a) Calculate the sum of the first 20 terms of the sequence;

b) Determine the 2013th term of the sequence;

c) Verify if 2013 is a term of the sequence.

Prof. Ecaterina Botan, prof. Contanu Mihai