The infinite sums of a sequence of numbers (or terms) is called a series. A sequence forms a pattern, these sequences can be identified through the patterns.
One important series (which happen to occur naturally in plants and nature) is Fibonacci series. The series go like this:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
As you can see, the number in any sequence is the sum of the two previous numbers - and it goes on forever!
A series follows a mathematical pattern and the terms can be described by a formula. We call any general or nth term of a series . where n stands for the number of the term and must be a positive integer.
For example, for the series 3 + 8 + 13 + 18 + 23 + ... find .
The first term is 3
Second term is 8 = 3 + 5 = 3 + 1 x 5
Third term is 13 = 3 + 5 + 5 = 3 + 2 x 5
Fourth term is 18 = 3 + 5 + 5 + 5 = 3 + 3 x 5
...and so on, following this pattern:
1. The nth term of a series is given by . Which term of the series is equal to 104?
2. The nth term of a series is given by . Find the value of n for the first negative term in the series.
For the first negative term, we want:
Since n is an integer, n=34 i.e. the 34th term is the first negative term.
3. The nth term of a series is given by the formula . Which term of the series is equal to 4095?
Series are often written in sigma notation () - which stands for the sum of a series. You may have seen this in finding the mean of a certain data in statistics.
2. Write 7 + 11 + 15 + ... + (4k + 3) in sigma notation.
The number of terms in the series is p - q + 1.