Proszę was o pomoc ;) chodzi o zadanie 3 tabelka

Wzory: [latex]a_n=a_1q^{n-1}[/latex] [latex]S_n=frac{a_1(q^n-1)}{q-1}[/latex] ______________________ [latex]a_1=2[/latex] [latex]q=3[/latex] [latex]S_n=242[/latex] [latex]242=frac{2cdot (3^n-1)}{3-1}[/latex] [latex]242=frac{2cdot (3^n-1)}{2}[/latex] [latex]242=3^n-1[/latex] [latex]3^n=242+1[/latex] [latex]3^n=243[/latex] [latex]3^n=3^5[/latex] [latex]n=5[/latex] [latex]a_5=2cdot 3^{5-1}=2cdot 3^4=2cdot 81=162[/latex] ______________________ [latex]q=frac{1}{2}[/latex] [latex]n=7[/latex] [latex]a_7=-frac{1}{2}[/latex] [latex]a_7=a_1cdot (frac{1}{2} )^{7-1}=a_1cdot (frac{1}{2})^6=a_1cdot frac{1}{64}[/latex] [latex]a_1cdot frac{1}{64}=-frac{1}{2}[/latex] [latex]a_1=-32[/latex] [latex]S_7=frac{a_1(q^7-1)}{q-1}=frac{-32cdot (( frac{1}{2} )^7-1)}{ frac{1}{2}-1}=[/latex] [latex]frac{-32cdot ( frac{1}{128}-1)}{- frac{1}{2}}=64cdot(- frac{127}{128})=- frac{127}{2}=-63,5[/latex] ______________________ [latex]q=2[/latex] [latex]n=10[/latex] [latex]S_{10}=1023[/latex] [latex]S_{10}=frac{a_1(2^{10}-1)}{2-1}=frac{a_1(1024-1)}{1}=1023a_1[/latex] [latex]1023a_1=1023[/latex] [latex]a_1=1[/latex] [latex]a_{10}=1cdot 2^{10-1}=2^9=512[/latex] ______________________ [latex]a_1=frac{1}{25}=5^{-2}[/latex] [latex]n=7[/latex] [latex]a_{7}=625[/latex] [latex]a_7=5^{-2}cdot q^{7-1}=5^{-2}cdot q^6[/latex] [latex]5^{-2}cdot q^6=625[/latex] [latex]q^6=625cdot 5^2[/latex] [latex]q^6=5^4cdot 5^2[/latex] [latex]q^6=5^6[/latex] [latex]q=5[/latex] [latex]S_7=frac{5^{-2}cdot (5^7-1)}{5-1}=frac{5^{-2}cdot (5^7-1)}{4}=frac{78125-1}{4cdot 5^2}=frac{78124}{100}=781,24[/latex] ______________________ [latex]a_1=sqrt{8}[/latex] [latex]q=-sqrt{2}[/latex] [latex]n=8[/latex] [latex]a_8=sqrt{8}cdot (-sqrt{2})^{8-1}=sqrt{8}cdot (-sqrt{2})^{7}=sqrt{8}cdot (-8 sqrt{2})=-32[/latex] [latex]S_8=frac{sqrt{8}cdot ((-sqrt{2})^8-1)}{-sqrt{2}-1}=frac{sqrt{8}cdot (16-1)}{-sqrt{2}-1}=frac{15sqrt{8}}{-sqrt{2}-1}=-frac{15sqrt{8}}{sqrt{2}+1}=[/latex] [latex]-frac{15sqrt{8}(sqrt{2}-1)}{(sqrt{2}+1)(sqrt{2}-1)}=30 sqrt{2}-60[/latex]