Question

sa se determine suma primilor n termeni ai progresiei aritmetrice a indice n daca
a1=5 a26=105 n=26

Answer 1

$\displaystyle a_1=5,~a_{26}=105,~n=26,~S_n=? \\ a_{26}=105 \Rightarrow a_{26-1}+r=105 \Rightarrow a_{25}+r=105 \Rightarrow a_1+25r=105 \Rightarrow \\ \Rightarrow 5+25r=105 \Rightarrow 25r=105-5 \Rightarrow 25r=100 \Rightarrow r= \frac{100}{25}\Rightarrow r=4 \\ S_{26}= \frac{2 \cdot 5+(26-1) \cdot 4}{2} \cdot 26 \\ S_{26}=(10+25 \cdot 4) \cdot 13 \\ S_{26}=(10+100) \cdot 13 \\ S_{26}=110 \cdot 13 \\ S_{26}=1430$