Question

Fie a₁=1, a₄=7 termenii unei progresii aritmetice. Calculati a₂₀₁₅.
va rog rezolvarea cu explicatii.

Answer 1

termenul general al unei progresii aritmetice este $a_{n} = a_{1} +(n-1)*r$
$a_{4}=1+3*r =\ \textgreater \ r=2 =\ \textgreater \ a_{2015}=1+2014*2=4029$

Answer 2

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