[tex]\text{The general term of arithmetic sequence}\ a_n=a_1+(n-1)d\\\\a_1-first\ term\\d-common\ difference\\\\a_1=1.77\\a_2=1.92\\a_3=2.07\\\vdots\\\\d=a_{n+1}-a_n\to d=a_2-a_1\\\\d=1.92-1.77=0.15\\\\\text{Substitute:}\\\\a_n=1.77+(n-1)(0.15)\qquad\text{use distributive property}\\\\a_n=1.77+(n)(0.15)+(-1)(0.15)\\\\a_n=1.77+0.15n-0.15\\\\a_n=0.15n+1.62\\\\31st\ term\to a_{31}\\\\\text{Substitute}\ n=31\ \text{to the equation of}\ a_n\\\\a_{31}=0.15(31)+1.62=4.65+1.62=6.27\\\\Answer:\ 31st\ term=6.27[/tex]
