Question

prog geometrice b1=2 b4=54 ,aflati b2015 si S2015

Answer 1

[tex]b_1=2,b_4=54\\ b_4=b_1\cdot q^3\\ 54=2\cdot q^3\\ q^3=27\Rightarrow q=3\\ b_{2015}=b_1\cdot q^{2014}\\ b_{2015}=2\cdot3^{2014}\\ -------\\ S_{2015}=b_1\cdot \frac{q^n-1}{q-1}\\ \\ S_{2015}=2\cdot\frac{3^{2015}-1}{3-1}\\ S_{2015}=3^{2015}-1[/tex]

Answer 2

b₁=2
b₄=54

bₓ=b₁*q⁽ˣ⁻¹⁾

b₄=b₁*q³
54=2*q³
q³=27
q³=3³
q=3

b₂₀₁₅=b₁*q²⁰¹⁴

b₂₀₁₅=2*3²⁰¹⁴

$S_n=\frac{b_1(1-q^n)}{1-q}$

$S_{2015}=\frac{2(1-3^{2015})}{1-3}=\frac{2(1-3^{2015})}{-2}=-1+3^{2015}$