Question

The 19th term of an arithmetic sequence is 64 and has a common difference of -3. What is the 152nd term ofthe sequence?

Answer 1

Step-by-step 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

`\begin{gathered} T_n=a+(n-1)d \\ n=19 \\ T_n=64 \\ d=-3 \end{gathered}`

So we will get the first term to be

`\begin{gathered} 64=a+(19-1)*-3 \\ 64=a+18*-3 \\ 64=a-54 \\ a=64+54 \\ a=118 \end{gathered}`

Finally, we will get the 152nd terms as

`\begin{gathered} T_(152)=118+(152-1)*-3 \\ T_(152)=118+151*-3 \\ T_(152)=118-453 \\ T_(152)=-335 \end{gathered}`

Therefore, the 152 nd term is -335

The answer is -335