5 uždavinys

Didėjančios geometrinės progresijos pirmasis narys lygus 2, o trečiasis lygus 18. Antrasis šios progresijos narys lygus:

A- 6 B 6 C 9 D 10

Sprendimas.

$b_{3}$ = $b_{2}\cdot q$ (1)

$b_{2}$ = $b_{1}\cdot q$ (2)

Pirmą lygtį padaliname iš antrosios:

b_₃

/ b_₂

b_₂* q

/ b_₁/ q

b_₃

/ b_₂

b_₂* q

/ b_₁/ q

$\frac{b_{3}}{b_{2}}$ = $\frac{b_{2}\cdot q}{b_{1}\cdot q}$

b_₃

/ b_₂

b_₂

/ b_₁

$\frac{b_{3}}{b_{2}}$ = $\frac{b_{2}}{b_{1}}$

b_₃ =

b_₂* b_₂

/ b_₁

$b_{3}$ = $\frac{b_{2}\cdot b_{2}}{b_{1}}$

b_₁* b_₃ = b_₂* b_₂ $b_{1}\cdot b_{3}$ = $b_{2}\cdot b_{2}$

b_₁* b_₃ = b_₂^² $b_{1}\cdot b_{3}$ = $b_{2}^{2}$

b_₂^² = b_₁* b_₃ $b_{2}^{2}$ = $b_{1}\cdot b_{3}$

saknis(

b_₂^²) = saknis(

b_₁* b_₃) $\sqrt {b_{2}^{2}}$ = $\sqrt {b_{1}\cdot b_{3}}$

b_₂ = saknis(

b_₁* b_₃) $b_{2}$ = $\sqrt {b_{1}\cdot b_{3}}$

b_₂ = saknis(

36) $b_{2}$ = $\sqrt {36}$

b_₂ = 6 $b_{2}$ = $6$

$\frac{b_{3}}{b_{2}}$ = $\frac{b_{2}\cdot q}{b_{1}\cdot q}$

$\frac{b_{3}}{b_{2}}$ = $\frac{b_{2}}{b_{1}}$

$b_{2}^{2}$ = $b_{1}\cdot b_{3}$

$b_{2}$ = $\sqrt {b_{1}\cdot b_{3}}$

$b_{2}$ = $\sqrt {2\cdot 18}$

$b_{2}$ = $\sqrt {36}$

$b_{2}$ = $6$

Atsakymas: B