The first term of a sequence is x 1equals1. each succeeding term is the sum of all those that come before it, x subscript n plus 1equalsx 1 plus x 2 plus times times times plus x subscript n. write out enough early terms of the sequence to deduce a general formula for x subscript n that holds for ngreater than or equals2.

The first term of the sequence is 1.
So,


Every next term is the sum of all the previous terms. So second term will also be 1.


Third term will be the sum of first two terms. So third term will be:


Fourth term will be the sum of first two terms. So fourth term will be:


Fifth term will be the sum of four two terms. So fifth term will be:


So the first 5 terms of the sequence will be:

1, 1, 2, 4, 8, ...

From second terms onward, a Geometric series is formed with a common ratio 2. The general formula for a geometric series can be written as:



Using the values, we get:



The above formula is valid for n equal to or greater than 2 and gives the general formula of the sequence.