Question

Find the 75th term of the arithmetic sequence -17, -13, -9....

Answer 1

Answer:

The 75th term of the arithmetic sequence -17, -13, -9.... is:

$a_{75}=279$

Step-by-step explanation:

Given the sequence

$-17, -13, -9....$

An arithmetic sequence has a constant difference 'd' and is defined by  

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$-13-\left(-17\right)=4,\:\quad \:-9-\left(-13\right)=4$

The difference between all the adjacent terms is the same and equal to

$d=4$

The first element of the sequence is:

$a_1=-17$

now substitute $d=4$ and $a_1=-17$ in the nth term of the sequence

$a_n=a_1+\left(n-1\right)d$

$a_n=4\left(n-1\right)-17$

$a_n=4n-21$

Now, substitute n = 75 in the $a_n=4n-21$ sequence to determine the 75th sequence

$a_n=4n-21$

$a_{75}=4\left(75\right)-21$

$a_{75}=300-21$

$a_{75}=279$

Therefore,  the 75th term of the arithmetic sequence -17, -13, -9.... is:

$a_{75}=279$