Question

помогите пж решить все задания

Answer 1

$2.\\a_1=\frac23,\;a_2=1\frac23,\;a_3=2\frac23\\\\a_2=a_1+d\Rightarrow d=a_2-a_1=1\frac23-\frac23=1\\a_{2012}=a_1+2011d=\frac23+2011=2011\frac23\\\\\\\\3.\;a_4=3,\;a_9=-17\\\\a_4=a_1+3d\Rightarrow a_1=a_4-3d\\a_{9}=a_1+8d\Rightarrow a_1=a_9-8d\\a_4-3d=a_9-8d\\3-3d=-17-8d\\8d-3d=-17-3\\5d=-20\\d=-4$

$4.\\b_1=-5,\;q=-5\\\\S_{n}=\frac{b_1(1-q^n)}{1-q}\\S_4=\frac{-5(1-(-5)^4)}{1-(-5)}=\frac{-5(1-625)}{6}=\frac{-5(-624)}6=\frac{3120}{6}=520\\\\\\5.\;b_3=-3,\;b_8=-96\\\\b_3=b_1\cdot q^2\Rightarrow b_1=\frac{b_3}{q^2}\\\\b_8=b_1\cdot q^7\Rightarrow b_1=\frac{b_8}{q^7}\\\\\frac{b_3}{q^2}=\frac{b_8}{q^7}\\\\\frac{q^7}{q^2}=\frac{b_8}{b_3}\\\\q^5=\frac{-96}{-3}=32\\\\q=\sqrt[5]{32}=2$

$6.\;b_1=\frac14,\;b_2=1,\;b_3=4\\\\b_2=b_1\cdot q\Rightarrow q=\frac{b_2}{b_1}=1:\frac14=1\cdot4=4\\\\S_5=\frac{\frac14(1-4^5)}{1-4}=\frac{\frac14(1-1024)}{-3}=\frac{-1023}{-12}=85\frac3{12}=85\frac14$