Question

sa se determine primul termen al unei progresii aritmetice de ratie 4 daca suma primilor 2 termeni=10

Answer 1

$a_{1}+a_{2}=10$
$a_{1}+a_{1}+r=10$
$2a_{1}+4=10$
$2a_{1}=6$
$a_{1}=3$

Answer 2

$\displaystyle r=4,~S_2=10,~a_1=? \\ S_2=10 \Rightarrow \frac{2a_1+(2-1) \cdot 4}{\not2} \cdot \not2=10 \Rightarrow 2a_1+1 \cdot 4=10 \Rightarrow \\ \Rightarrow 2a_1+4=10 \Rightarrow 2a_1=10-4 \Rightarrow 2a_1=6 \Rightarrow a_1= \frac{6}{2} \Rightarrow \boxed{a_1=3}$