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1andrusha1
a fost răspuns

determinati primul termen si ratia progresiei geometrice daca[tex] \left \{ {{b4-b2=18} \atop {b5-b3=36}} \right. [/tex]

Răspuns :

C04f
Se exprima si aici toti termenii in functie de primul si ratia progresiei geometrice, cu formula:  [tex] b_{n}= b_{1}* q^{n-1} [/tex]
Vezi imaginea C04f
[tex]\it b_4-b_2 = 18 \Longrightarrow b_2q^2-b_2=18 \Longrightarrow b_2(q^2-1)=18\ \ \ \ (1)[/tex]

[tex]\it b_5-b_3 = 36 \Longrightarrow b_3q^2-b_3=36 \Longrightarrow b_3(q^2-1)=36\ \ \ \ (2)[/tex]

[tex]\it (1),\ (2) \Longrightarrow \dfrac{b_3}{b_2} =\dfrac{36}{18} \Longrightarrow \dfrac{b_3}{b_2} = 2 \Longrightarrow \dfrac{b_2q}{b_2}=2 \Longrightarrow q = 2 \ \ \ \ (3)[/tex]

[tex]\it (1), (2) \Longrightarrow b_2(2^2-1) =18 \Longrightarrow b_2\cdot3=18 \Longrightarrow b_2 =6 \Longrightarrow b_1q=6 [/tex]

[tex]\it \Longrightarrow b_1\cdot2=6 \Longrightarrow b_1=3[/tex]




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