James has noticed that the number of new tree branches that have grown on a tree in his backyard each year follows the sequence 1,3,5,7,… meaning there was

Question

James has noticed that the number of new tree branches that have grown on a tree in his backyard each year follows the sequence 1,3,5,7,… meaning there was 1 new branch at 0 years, 3 new branches at 1 year, 5 new branches at 2 years, and so on.

If f(n) represents the sequence, determine the number of new branches the tree will have at 10 years.

Enter the value of f(n) at f(10).

f(10)= [blank] −−−−−− branches

The answer I got was 21, but I am not entirely sure if that is correct because I also received the answers 19 and 23. Help would be great appreciated. 

Answer 1

The problem depends of how you number the terms.

(0,1) (1,3) (2,5) is a_n = 1+2n and so (10,21) is in this set and is the 11th term.

If you number the terms differently, you will get a different answer.