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Sa se determine suna primilor trei termeni ai unei progresii geometrice stiind ca suma primilor doi termeni ai progresiei este egala cu 8 iar
diferenta dintre al doilea termen si primul termen este egala cu 4.

Răspuns :

Miky93
[tex]a_1+a_2=8 \\ a_2-a_1=4 \ \ ===\ \textgreater \ \underline{a_2=4+a_1} \\\\\\ a_1+4+a_1=8 \\\\ 2a_1=4 \\\\ \boxed{a_1=2} \\\\\ a_2=8-a_1 \\\\\ \boxed{a_2=6} \\\\\\ a_3=a_2*r \\\\\\ r=\frac{a_2}{a_1} \to \frac{6}{2}=3 \\\\ \underline{r=3} \\\\\ a_3=6*3 \\\\ \boxed{a_3=18} \\\\\\ S_3=2+6+18 \\\\ \boxed{\boxed{ S_3= 26}}[/tex]
 
 [tex]\it \dfrac{..}{..}[/tex]


[tex]\it a_2+a_1= 8\ \ \ \ (1)[/tex]

[tex]\it a_2-a_1=4\ \ \ \ (2)[/tex]

[tex]\it(1), (2) \Longrightarrow a_1= 2,\ a_2=6[/tex]

[tex]\it Ratia\ este\ q = \dfrac{a_2}{a_1} =\dfrac{6}{2} =3[/tex]

[tex]\it a_3 = a_2\cdot q=6\cdot3=18[/tex]

[tex]\it a_1+a_2+a_3 = 2+6+18 =26[/tex]




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