Question

The first three terms of an arithmetic sequence are as follows.

Answer 1

Answer:

The next terms of the sequence 33, 25, 17 is:

$a_4=9$

$a_5=1$

Step-by-step explanation:

$3, 25, 17...$

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

$25-33=-8,\:\quad \:17-25=-8$

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

$d=-8$

The first element of the sequence is:

$a_1=33$

now substituting $a_1=33$ and $d=-8$ in the nth term

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

$a_n=-8\left(n-1\right)+33$

$a_n=-8n+41$

Determining the 4th term:

We already got the nth term of the Arithmetic sequence

$a_n=-8n+41$

substitute n = 4

$a_4=-8\left(4\right)+41$

$a_4=-32+41$

$a_4=9$

Determining the 5th term:

substitute n = 5 in the nth term

$a_n=-8n+41$

$a_5=-8\left(5\right)+41$

$a_5=-40+41$

$a_5=1$

Thus, the next terms of the sequence 33, 25, 17 is:

$a_4=9$

$a_5=1$