Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, ...?
We will use the concept of arithmetic progression in order to find the general term.
Answer: The general term is given by an = 2n - 1
Let us see how we will use the concept of arithmetic progression in order to find the general term.
The sequence that is given to us is 1, 3, 5, 7, 9, ...
a1 = 1, a2 = 3, a3 = 5, a4 = 7, a5 = 9
Now we can see that a2 - a1 = 2, a3 - a2 = 2, a4 - a3 = 2, a5 - a4 = 2.
Hence, we can see that the common difference is 2.
Therefore nth term of an arithmetic progression whose first term a1 = 1 and common difference d = 2 is given by,
an = a1 + (n - 1) d