Question

Геометрическая прогрессия: b1=512,bn=1,Sn=1023. Найти и n;q

Answer 1

b1 = 512;    bn = 1;    Sn = 1023;

Sn = (bn · q - b1)/(q - 1)

1023 = (q - 512)/(q - 1)

1023q - 1023 = q - 512

1022q = 511

q = 1/2

bn = b1 · q^(n - 1)     1 = 512 · (1/2)^(n -1)      1/512 = 1/2^(n - 1)

1/2^9 = 1/2^(n - 1)

9 = n - 1

n = 10

Ответ: n = 10; q = 1/2