Question

Va rog cat mai corect! Dau coroana!

Answer 1

b1,b2,b3,...,bn progresie geometrică

b2 = 8

b1/b5 = 1/16

___________

b1 = ?

___________

folosim formula: bn = b1 • q^(n-1)

b5 = b1 • q⁴

din ipoteza: b1/b5 = 1/16 ←→ b1/b1 • q⁴ = 1/16

←→ 1/q⁴ = 1/16

←→ q⁴ = 16

16 = 2⁴ sau (-2)⁴

q1 = 2

sau

q2 = -2

b2 = b1 • q → b1 = b2/q

• Pentru q1 = 2 avem:

b1 = 8/2 = 4

• Pentru q2 = - 2 avem:

b1 = 8/-2 = - 4

Answer 2

$\it \dfrac{..}{..}\ \ \ b_2=8;\ \ \ \dfrac{b_1}{b_5}=\dfrac{1}{16} \Rightarrow \dfrac{b_1}{b_1\cdot q^4}=\dfrac{1}{2^4} \Rightarrow q^4=2^4 \Rightarrow q=\pm2\\ \\ \\ q=-2\Rightarrow b_1=\dfrac{b_2}{q}=\dfrac{8}{-2}=-4\\ \\ \\ q=2\Rightarrow b_1=\dfrac{b_2}{q}=\dfrac{8}{2}=4$