# What is an arithmetic sequence whose common difference is -10?Was on my exam but still don't understand the question.

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An arithmetic sequence:

a1, a2, a3, a4,.....,an,..., where

a2=a1+ r

a3=a2 + r= (a1 + r) + r= a1+ 2r

a4= a3 + r= a1 + 3r

..........................

an= a1 + (n-1)r

where r is the common difference

r = -10

a2= a1 + (-10)= a1 - 10

a3= a1 - 2X10

a4= a1 - 3X10

...................

an= a1 - nX10

Let's name the first term x1

So, the common difference is -10, lets name it c

So, the second term would be x1+c= x1+(-10)=x1-10

The third term would be x1+c+c= x1-10-10= x1-20

The forth term would be like x1+c+c+c= x1-10-10-10= x1-30

So, you might have guessed the nth term, which is:

nth term= x1+(n-1)*-10

The arthimetic sequence would be

x1, x1-10, x1-20, x1-30...... x1+(n-1)^-10.