Question

Find the 75th term of the arithmetic sequence
16, 15, 14,

Answer 1

`a_(75)=-58`

Explanation:

This is an arithmetic sequence:

`a_n=a_1+(n-1)d`

where d is the common difference and n is the index of any given term.

For the given sequence, the common difference is -1:

`15-16=-1\\14-15=-1`

Knowing both the common difference and the first term, you can write the equation for this sequence:

`a_n=16+(n-1)(-1)`

Then you can use that equation to find the 75th term:

`a_(75)=16+(75-1)(-1)\\a_(75)=16+(74)(-1)\\a_(75)=16-74\\a_(75)=-58`