Question

a1= 1, a4=7 termenii unei progresii aritmetice. Calculati a2015.

Answer 1

$\displaystyle a_1=1,~a_4=7,~a_{2015}=? \\ \\ a_4=7 \Rightarrow a_{4-1}+r=7 \Rightarrow a_3+r=7 \Rightarrow a_1+3r=7 \Rightarrow 1+3r=7 \Rightarrow \\ \\ \Rightarrow 3r=7-1 \Rightarrow 3r=6 \Rightarrow r= \frac{6}{3}\Rightarrow r=2 \\ \\ a_{2015}=a_{2015-1}+r=a_{2014}+r=a_1+2014r=1+2014 \cdot 2= \\ \\ =1+4028=4029 \\ \\ \boxed{a_{2015}=4029}$