Question

What is the answer???

Answer 1

`Method\ 2:\\\\a_n=a_(n-1)+(1)/(2)\\\\\text{It's an arithmetic sequencion where}\ a_1=-(3)/(2)\ \text{and common difference}\ d=(1)/(2).\\\\\text{The formula of n-th term is}\ a_n=a_1+(n-1)d.\ \text{Substitute}\\\\a_n=-(3)/(2)+(n-1)\left((1)/(2)\right)=-(3)/(2)+(1)/(2)n-(1)/(2)=-(4)/(2)+(1)/(2)n=(1)/(2)n-2\\\\a_9=(1)/(2)(9)-2=4.5-2=2.5=(5)/(2)`
`a_1=-(3)/(2)\\\\a_n=a_(n-1)+(1)/(2)\\\\Method\ 1:\\\\a_2=a_1+(1)/(2)\to a_2=-(3)/(2)+(1)/(2)=-(2)/(2)\\\\a_3=a_2+\dfraC{1}{2}\to a_3=-(2)/(2)+(1)/(2)=-(1)/(2)\\\\a_4=a_3+(1)/(2)\to a_4=-(1)/(2)+(1)/(2)=0\\\\a_5=a_4+(1)/(2)\to a_5=0+(1)/(2)=(1)/(2)\\\\a_6=a_5+(1)/(2)\to a_6=(1)/(2)+(1)/(2)=(2)/(2)\\\\a_7=a_6+(1)/(2)\to a_7=(2)/(2)+(1)/(2)=(3)/(2)`

`a_8=a_7+(1)/(2)\to a_8=(3)/(2)+(1)/(2)=(4)/(2)\\\\a_9=a_8+\dfraC{1}{2}\to a_9=(4)/(2)+(1)/(2)=(5)/(2)`