Question

Гкометрическая прогрессия b₁=5 q=3 Sn=200 n-?

Answer 1

$S_n = frac{b_1(1-q^n)}{(1-q)}</var>;$<br /><br /><img src=[/tex]S_n(1-q)=b_1(1-q^n);" title="S_n = frac{b_1(1-q^n)}{(1-q)};" title="S_n(1-q)=b_1(1-q^n);" title="S_n = frac{b_1(1-q^n)}{(1-q)};" alt="S_n(1-q)=b_1(1-q^n);" title="S_n = frac{b_1(1-q^n)}{(1-q)};" />

$S_n = frac{b_1(1-q^n)}{(1-q)}</var>;$

$<var>S_n(1-q)=b_1(1-q^n);$

$S_n-S_nq=b_1-b_1q^n;$

$S_n-S_nq-b_1=-b1q^n</var>;$

$S_n-S_nq=b_1-b_1q^n;$

$<var>S_n(1-q)=b_1(1-q^n);$

$S_n-S_nq=b_1-b_1q^n;$

$S_n-S_nq-b_1=-b1q^n</var>;$

$<var>q^n=frac {S_n-S_nq-b_1}{-b_1};$

$S_n-S_nq-b_1=-b1q^n</var>;$

$<var>q^n=frac {S_n-S_nq-b_1}{-b_1};$

$3^n=frac{(200-200*3-5)}{-5}</var>;$

$<var>q^n=frac {S_n-S_nq-b_1}{-b_1};$

$3^n=frac{(200-200*3-5)}{-5}</var>;$

$<var>3^n=81;$

$3^n=frac{(200-200*3-5)}{-5}</var>;$

$<var>3^n=81;$

$<var></var>n = 4;" title="<var>3^n=81;" /> [tex]<var></var>n = 4;" alt="<var>3^n=81;" /> [tex]<var></var>n = 4;" /><var></var> <em>Ответ:</em> [tex]<var></var>n = 4.$