Question

Progresii artimetice
a₂₃=32 si a₃₂=23, calculati a₁ si r.

Answer 1

$\displaystyle a_{23}=32,~a_{32}=23,~a_1=?,~r=?\\ \\a_{23}=32\Rightarrow a_{23-1}+r=32\Rightarrow a_{22}+r=32 \Rightarrow a_1+22r=32 \Rightarrow \\ \\ \Rightarrow a_1=32-22r\\ \\a_{32}=23\Rightarrow a_{32-1}+r=23 \Rightarrow a_{31}+r=23 \Rightarrow a_1+31r=23 \Rightarrow \\ \\\Rightarrow 32-22r+31r=23 \Rightarrow -22r+31r=23-32 \Rightarrow 9r=-9 \Rightarrow\\ \\ \Rightarrow r=-\frac{9}{9} \Rightarrow \boxed{r=-1}\\ \\ a_1=32-22r\Rightarrow a_1=32-22\cdot (-1) \Rightarrow a_1=32+22 \Rightarrow \boxed{a_1=54}$

Answer 2

a₂₃=a₁ +22r=32
a₃₂=a₁ +31r
{a₁ +22r=32
{a₁ +31r=23
Scazi a₁+22r=32 din a₁+31r=23 și dă:
{ 9r=-9
{ a₁+22r=32 =>

{ r=-9:9=-1
{ a₁-22=32

{ r=-1
{ a₁=32+22=54

Succes!! :*