How do you find the next three terms of the arithmetic sequence #22, 20, 18, 16,...#?

1 Answer
Apr 5, 2018

Answer:

#color(blue)(12,10,8)#

Explanation:

The #nth# term of an arithmetic sequence is given by:

#a+(n-1)d#

Where:

#bba# is the first term.

#bbd# is the common difference.

#bbn# is the #nth# term.

If #a,b,c# are in arithmetic sequence, then:

#b-a=c-b#

This is called the common difference:

We have:

#22,20,18,16,...#

#:.#

#20-22=18-20=-2#

#d=-2#

First term is #20#

#a=20#

We need 5th , 6th and 7th terms:

Using:

#a+(n-1)d#

#5th=20+(5-1)(-2)=12#

#6th=20+(6-1)(-2)=10#

#7th=20+(7-1)(-2)=8#

#:.#

#22,20,18,16,color(blue)(12,10,8,)...#