Question

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

Answer 1

Answer:

$a_{75}=-58$

Step-by-step 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:

$a_{75}=16+(75-1)(-1)\\a_{75}=16+(74)(-1)\\a_{75}=16-74\\a_{75}=-58$