Запишите формулу n-ого члена последовательности 1) 2; 3 1/2; 5; 6 1/2 ...; a=?2)...

1) 2; 3 1/2; 5; 6 1/2 ...; a=?

$a_{n} =a_{1} +d(n-1)=2+1.5(n-1)=1.5n+0.5\\ a_{1} =1.5*1+0.5=2\\a_{2} =1.5*2+0.5=3.5\\a_{3} =1.5*3+0.5=5\\a_{4} =1.5*4+0.5=6.5\\$

2) 1/3;2/3;1;1 1/3;1 2/3;...; c=?

$c_{n} =c_{1} +d(n-1)=\frac{1}{3} +\frac{1}{3} (n-1)=\frac{n}{3} \\ c_{1} =1/3\\ c_{2} =2/3\\ c_{3} =3/3=1\\ c_{4} =4/3=1\frac{1}{3} \\ c_{5} =5/3=1\frac{2}{3}$

3) 5; 0,5;0,05;0,005;....;a=?

$a_{n} =5*0.1^{n-1}\\a _{1} =5*0.1^0=5\\a _{2} =5*0.1^{2-1}=5*0.1=0.5\\ a _{3} =5*0.1^{3-1}=5*0.1^2=0.05\\a _{4} =5*0.1^{4-1}=5*0.1^3=0.005\\ \\$