How do you write a rule for the nth term of the arithmetic sequence #a_11=29, a_20=101#?

1 Answer
Aug 19, 2017

Answer:

#a_n=8n-59#

Explanation:

Let set up two equation base on the information that given
#a_11=29 n=11# , #29=a_1+(11-1)d# , #29=a_1+10d#

#a_20=101#, #101=a_1+(20-1)d# , #101=a_1+19d#

Now we got:
#101=a_1+19d#
#29=a_1+10d#
We can solve this by using elimination method
So we need to multiply either equation to isolate #a_1#
#101=a_1+19d#
#-29=-a_1-10d#
Add vertically
#72=9d# We can find d (common ratio) by divide 9 on both sides
#d=8#
Now substitute d into either equation that we set up to find #a_1#
#29=a_1+10(8)#
#29=a_1+80#
#a_1=-51#

The rule for an Arithmetic Sequence is #a_n=a_1+(n-1)d#
#d=8# #a_1=-51#
#a_n=-51+(n-1)8#
#a_n=-51+8n-8#
#a_n=8n-59#