Find 57th term Given:
[tex]-51,-39,-27,-15,\ldots[/tex]From the given sequence
There is a common difference of
[tex]-39-(-51)=-27-(-39)=12[/tex]Therefore, the common difference is 12
Hence, the sequence is an arithmetic sequence
The nth term of an arithmetic sequence is given as
[tex]T_n=a+(n-1)d[/tex]Where
a = first term
d = common difference
n = number of terms
Hence,
[tex]n=57,a=-51,d=12[/tex]Substituting these values gives
[tex]T_{57}=-51+(57-1)12[/tex]Solve the equation
[tex]\begin{gathered} T_{57}=-51+(56)12 \\ T_{57}=-51+672 \\ T_{57}=621 \end{gathered}[/tex]Therefore, the 57th term is 621
