Respuesta :
Explanation
We are told to find the 152nd term
to do so, we will use the information given
Firstly, we are told that
The 19th term of an arithmetic sequence is 64 and has a common difference of -3.
So, using the formula
[tex]\begin{gathered} T_n=a+(n-1)d \\ n=19 \\ T_n=64 \\ d=-3 \end{gathered}[/tex]So we will get the first term to be
[tex]\begin{gathered} 64=a+(19-1)\times-3 \\ 64=a+18\times-3 \\ 64=a-54 \\ a=64+54 \\ a=118 \end{gathered}[/tex]Finally, we will get the 152nd terms as
[tex]\begin{gathered} T_{152}=118+(152-1)\times-3 \\ T_{152}=118+151\times-3 \\ T_{152}=118-453 \\ T_{152}=-335 \end{gathered}[/tex]Therefore, the 152 nd term is -335
The answer is -335
