2. Find the eleventh term of the arithmetic progression if the sum of the first seven terms $S_{7}=77$, and the first term $a_{1}=5$.
Solution: $S_{7}=77 ; a_{1}=5, a_{11}=$ ?

$S_{7}=\frac{2 a_{1}+d(7-1)}{2} \cdot 7=\frac{10+6 d}{2} \cdot 7=(5+3 d) 7=77 \Rightarrow d=2, a_{11}=a_{1}+10 d=25$.