Question

What is the 57th term of -51, -39, -27, -15,...

Answer 1

Find 57th term Given:

`-51,-39,-27,-15,\ldots`

From the given sequence

There is a common difference of

`-39-(-51)=-27-(-39)=12`

Therefore, the common difference is 12

Hence, the sequence is an arithmetic sequence

The nth term of an arithmetic sequence is given as

`T_n=a+(n-1)d`

Where

a = first term

d = common difference

n = number of terms

Hence,

`n=57,a=-51,d=12`

Substituting these values gives

`T_(57)=-51+(57-1)12`

Solve the equation

`\begin{gathered} T_(57)=-51+(56)12 \\ T_(57)=-51+672 \\ T_(57)=621 \end{gathered}`

Therefore, the 57th term is 621