Question

найдите сумму первых 5 членов геометрической прогрессии:
5)-32;16;...;
6)1;-1/2;...;
8)с1=1;q=-2

Answer 1

5) b1=-32, b2=16, q=b2÷b1=16÷(-32)=-0,5
$s5 = \frac{b1( {q}^{5} - 1)}{q - 1} = \frac{ - 32( {( - 0.5)}^{5} - 1) }{ - 0.5 - 1} = \\ \frac{ - 32 \times ( - 1 \frac{1}{32} )}{ - 1.5} = \frac{ 33}{ - 1.5} = - 22$
6) b1=1, b2=-1/2, q=b2/b1=-1/2÷1=-1/2
$s5 = \frac{1( {( - 0.5)}^{5} - 1}{ - 0.5 - 1} = \frac{ - 1 \frac{1}{32} }{ - 1.5} = \\ - \frac{33}{32} \div ( - \frac{3}{2} ) = \frac{33}{32} \times \frac{2}{3} = \frac{11}{16}$
8) c1=1, q=-2
$s5 = \frac{1( {( - 2)}^{5} - 1}{ - 2 - 1} = \frac{ - 32 - 1}{ - 3} = \frac{ - 33}{ - 3} = 11$