Question

Дают 85 баллов. Найдите шестой и n-ый член геометрической прогрессии:
а)48; 12; ...
б) дробь 64 деленнач на 9; дробь -32 деленное на 3;...
в) -0.001; -0.01; ...
г) -100; 10; ...

Answer 1

а) 48, 12,...

b1 = 48, q = 1/4

b6 = b1*q^5 = 48/4^5 = 3/64

bn = b1*q^(n-1) = 48/4^(n-1) = 3*(4^(3-n))



б) 64/9, -32/3...

b1 = 64/9, q = - 3/2

b6 = b1*q^5 = - 64*243/(9*32) = -54

bn = b1*q^(n-1) = (64/9)*(-3/2)^(n-1)



в) -0,001; -0,01...

b1 = -0,001; q = 10

b6 = b1*q^5 = -0,001*10^5 = -100

bn = b1*q^(n-1)= -0,001* 10^(n-1) = -10^(n-4)



г) -100, 10....


b1= -100; q = -0,1

b6 = b1*q^5 = 100 *(-10)^(-5) = -0,001

bn = b1*q^(n-1) = 100*(-0,1)^(n-1)

Answer 2

а) 48, 12, ,,,   
d = 12 / 48 = 1/4
b6 = b1 * d^5 = 48 * (1/4)^5 = 48/1024 = 6/128=3/64
bn = b1 * (1/4)^(n-1)$b_n = b_1* (frac{1}{4})^{n-1}$
б) $frac{64}{9}; - frac{32}{3} \ d=- frac{32}{3}: frac{64}{9}=- frac{32}{3}* frac{9}{64}=- frac{3}{2} \ b_6= frac{64}{9}*(- frac{3}{2})^5= -frac{64}{9}* frac{3^5}{2^5}= -frac{64}{9}* frac{243}{32}= -54 \ b_n=b_1*(- frac{3}{2})^{n-1}$
в)$-0.001; -0.01 \ d=-0.01:(-0.001)=10 \ b_6=(-0.001)*10^5=-100 \ b_n=(-0.001)*10^{n-1}$
г)$-100, 10 \ d=10:(-100)=-0.1 \ b_6=-100*(-0.1)^5=-100*(-0.00001)=0.001 \ b_n=-100*(-0. 1)^{n-1}$