Witam, potrzebuję pilnie na już!!!! Dam naj za pełne rozwiązania Zadania w załączniku

1. a) [latex]a_n=4n-7 \ a_1=-3 \ a_2=1 \ a_3=5 [/latex] tak jest to ciąg arytmetyczny o r=4 b) [latex]a_n=1-2n \ a_1=-1 \ a_2=-3 \ a_3=-5[/latex] jest to ciąg arytmetyczny o różnicy r=-2 c) [latex]a_n=3^{n-1}[/latex] [latex]a_1=3^{0}=1[/latex] [latex]a_2=3[/latex] [latex]a_3=9[/latex] nie jest to ciąg arytmetyczny 2. [latex]a_1=2 \ a_2=a_1+r \ 4=2+r \ r=2 \ a_7=a_1+6r \ a_7=2+12 \ a_7=14[/latex] [latex]S_7= frac{a_1+a_n}{2}*n[/latex] [latex]S_7=frac{2+14}{2}*7[/latex] [latex]S_7=8*7[/latex] [latex]S_7=56[/latex] 3. [latex]a_1=3 \ a_2=a_1+r \ 7=3+r \ r=4[/latex] [latex]a_{31}=a_1+30r \ a_{31}=3+120[/latex] [latex]a_{31}=123 \ S_{31}= frac{a_1+a_{31}}{2}*n[/latex] [latex]S_{31}= frac{3+123}{2}*31[/latex] [latex]S_{31}=63*31[/latex] [latex]S_{31}=1953[/latex] 4.a [latex]a_1=7 \ a_2=11 \ r=4[/latex] [latex]a_n=a_1+(n-1)r \ 51=7+4n-4[/latex] [latex]48=4n \ n=12[/latex] [latex]S_{12}=frac{7+51}{2}*12[/latex] [latex]S_{12}=348[/latex] 4.b [latex]a_1=-5 \ a_2=-7 \ r=-2 \ a_n=a_1+(n-1)r \ -31=-5-2n+2 \ -28=-2n \ n=14 \ S_{14}= frac{-5-31}{2} *14 \ S_{14}=-36*7 \ S_{14}=252[/latex] 5.a [latex] left { {{a_4=a_1+3r} atop {a_8=a_1+7r}} ight. \ left { {{6=a_1+3r} atop {14=a_1+7r}} ight. \ left { {{a_1=6-3r} atop {14=6-3r+7r}} ight. \ left { {{a_1=6-3r} atop {8=4r}} ight. \ left { {{r=2} atop {a_1=0} ight.[/latex] [latex]a_{10}=0+9*2 \ a_{10}=18 \ S_{10}= frac{18}{2} *10 \ S_{10}=90[/latex] 5.b [latex] left { {{1=a_1+5r} atop {3=a_1+7r}} ight. \ left { {{a_1=1-5r} atop {3=1-5r+7r}} ight. \ left { {{r=1} atop {a_1=-4}} ight. \ [/latex] [latex]a_{10}=-4+9r \ a_{10}=5 \ S_{10}= frac{-4+5}{2}*10 \ S_{10}=5[/latex] 6.a [latex]a_1=-27 \ a_2=9 \ 9=-27q \ q= -frac{1}{3}[/latex] [latex]przyklad_1=1 \ przyklad_2=-frac{1}{3}[/latex] 6b [latex]a_1=1 \ a_2=-2 \ -2=q \ przyklad_1=4*(-2)=-8 \ przyklad_2=-8*(-2)=16[/latex] 6c [latex]a_1=64 \ a_2=16 \ 16=64q \ q= frac{1}{4} \ przyklad_1=4* frac{1}{4} =1 \ przyklad_2= frac{1}{4}[/latex] 7a [latex]a_1=5 \ a_2=-5 \ a_3=5 \ a_4=-5 \ a_5=5[/latex] 7b Nie ma 7c [latex]a_1=16 \ a_2=8 \ a_3=4 \ a_4=2 \ a_5=1[/latex] 8. [latex]a_1=3 \ a_2=6 \ 6=3r \ r=2[/latex] [latex]a_{n}=a_1*q^{n-1} \ a_{11}=a_1*q^{10} \ a_{11}=3*1024 \ a_{11}=3072[/latex] 9a. [latex]a_1=-2 \ q=-3 \ a_5=-2*(-3)^4 \ a_5=-2*81=-162[/latex] 9b. [latex]a_1=-7 \ q=-1 \ a_{15}=-7*(-1) \ a_{15}=7[/latex] 10 [latex]a_1=128 \ a_2=64 \ 64=128q \ q= frac{1}{2} \ a_n=128* frac{1}{2} ^{n-1} \ a_7=128* (frac{1}{2})^6 \ a_7=2[/latex] 11. [latex] left { {{7=a_1*q} atop {28=a_1*q^3}} ight. \ left { {{a_1= frac{7}{q} } atop {28={ frac{7}{q} *q^3}} ight. \ left { {{{a_1= frac{7}{q} } atop {28=7q^2}} ight. \ left { {{{a_1= frac{7}{q} } atop {q=2}} ight. [/latex] lub [latex]q=-2[/latex] [latex]a_1=3,5 \ lub \ a_1=-3,5[/latex] [latex]a_n=3,5*2^{n-1} \ lub \ a_n=-3,5*-2^{n-1}[/latex] 12.a Nie ma danych 12.b [latex]a_1=16 \ a_2=8 \ q= frac{1}{2} \ S_n=a_1* frac{1-q^n}{1-q} \ S_8=16* frac{1- frac{1}{256} }{0,5} \ S_8=32* frac{255}{256} = frac{255}{8} [/latex] 12.c [latex]a_1=15 \ a_2=-30 \ q=-2 \ S_8=15* frac{1-256}{3} \ S_8=5*(-255)=-1275[/latex] 13a. [latex]a_1=2 \ a_2=8 \ r=4 \ S_5=2* frac{1-256}{-3} =2* frac{255}{3} =170[/latex] 13b. [latex]a_1=8[/latex] [latex]a_2=4[/latex] [latex]r= frac{1}{2}[/latex] [latex]S_5=8* frac{1- frac{1}{16} }{0,5} =16* frac{15}{16} =15[/latex] 13c. [latex]a_1=-2[/latex] [latex]a_2=-6[/latex] [latex]q=3[/latex] [latex]S_5=-2*frac{1-81}{-2} =4*(-80)=-320[/latex]