Zadania z ciągu arytmetycznego, prosze o pomoc, zadania w załączniku.

[latex] 1.a_{2}=12 \ a_{4} =54 \ a1+r=12 \ a1+3r=54 \ a1=12-r \ 12-r+3r=54 \ 2r=42 \ r=21 \ a1=-9 \ a_{n} =-9+(n-1)*21=21n-30 \ 2. a_{n}= n^{2} +3n-2 \ a_{n+1} = (n+1)^{2} +3(n+1)-2 \ a_{n+1} - a_{n} = n^{2} +2n+1+3n+3-2- n^{2} -3n-2=2n eq const \ \ 3. a1+5r=8 \ -2+5r=8 \ 10=5r \ r=2 \ S_{15} = frac{-4+14*2}{2} *15 \ S_{15}=180 \ 4. a1=2  r=4 \ S_{150} =(4+149*4)/2 *150 \ S_{150} =45000[/latex]