Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Thank you for watching the preview.
To unlock all 5,300 videos, start your free trial.
Arithmetic Sequences  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Finding the general term for an arithmetic sequence when we don’t really know the first term or the difference. There’s a couple ways of doing this.
The first way the way I’m going to focus on right now is we are basically just given two numbers right next to each other, we are given the 20th term of the sequence and the 20st term of the sequence. So using those two I can easily find the difference. I went up one term number and I went up three units, so what this tells me is that my common difference is just 3.
I then need to make a equation using the general term to find my first term. So what the general term is is a sub n is equal to a sub 1 plus n minus 1 times d. And we can choose either one of these pieces of information to plug in in order to solve for a sub 1, the piece of information we're missing. I’m going to choose to work with a sub 21 because this is representing n so when I plug the 21 in here 21 minus 1 gives us 20 which is a lot nicer number than if I plug this is 20 minus 1 then I’m dealing with a 19.
You get the exact same answer but just to make our numbers easier I’m going to go with this one. So we know we are dealing with this term and the actual term is 104. So we can plug that in for a sub n a sub 1 is what we don’t know, it’s what I need to find plus n minus 1, the 21 is our nth term so this is just going to be 21 minus 1 which is 20 and times our d which we know to be 3.
We now have enough information to solve for a1, 104 that is equal to a1 plus 21 minus 20 times 3 is 60 so a1 is equal to 104 minus 60 which is just 44.
So now I have enough information to make my general term. I know my first term and I know my d, so I just have to plug those into the equation leaving me with a sub n is equal to a1 which we just found to be 44, plus n minus 1 times d which we know to be 3.
So taking some information, finding our missing link and then putting it together to find our general term.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Concept (1)
Sample Problems (19)
Need help with a problem?
Watch expert teachers solve similar problems.

Arithmetic Sequences
Problem 1 11,204 viewsGiven 11, 7, 3...
Find a_{301}. 
Arithmetic Sequences
Problem 2 8,571 viewsGiven a_{20} = 101 and a_{21} = 104,
find the general term, a_{n}. 
Arithmetic Sequences
Problem 3 7,932 viewsGiven a_{11} = 52, a_{19} = 92,
find a_{1001} 
Arithmetic Sequences
Problem 4 7,426 viewsFind the number of terms:
7 , 13 , 19 ... 85 3 3 3 3 
Arithmetic Sequences
Problem 5 1,285 views 
Arithmetic Sequences
Problem 6 1,369 views 
Arithmetic Sequences
Problem 7 1,208 views 
Arithmetic Sequences
Problem 8 1,584 views 
Arithmetic Sequences
Problem 9 1,021 views 
Arithmetic Sequences
Problem 10 945 views 
Arithmetic Sequences
Problem 11 1,081 views 
Arithmetic Sequences
Problem 12 958 views 
Arithmetic Sequences
Problem 13 895 views 
Arithmetic Sequences
Problem 14 934 views 
Arithmetic Sequences
Problem 15 908 views 
Arithmetic Sequences
Problem 16 937 views 
Arithmetic Sequences
Problem 17 960 views 
Arithmetic Sequences
Problem 18 895 views 
Arithmetic Sequences
Problem 19 895 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete