Question 215264
Sequence is 10, 6,2,-2,-6.  I have to find the nth term, the 12th term and 27th term.


Step 1.  Look for a pattern.  Difference between 10 and 6 is 4.  The difference of 6 and 2 is also 4.  Difference between 2 and -2 is also four, and the difference between -2 and -6 is four.  


Step 2.  So first term is 10 need to subtract 4 to get 6. 10 - 4(n-1) where n=2 for 6.  


Step 3.  See if  the formula works for the rest of the sequence.  10-4(n-1)= 10-4n-1=11-4n (as we mention in Step 1, the difference is 4.  Now we know the first term is 10 so when n is 1 we get 10 since 10-4(1-1)=10.  When n is 2, we get 6 since 10-4(2-1)=6. When n is 3, we get 10-4*(3-1)=-2.  For n=4, we get 10-4*(4-1)=-6. So the formula works. 


Step 4.  ANSWER:  The equation for the sequence is 10-4(n-1) or 11-4n


Step 5.  ANSWER.  For n=12, then 11-4n=11-4*12=-37


Step 5.  ANSWER:  For n=27, then 11-4n=11-4*27=-97


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J