Sequence formula mainly refers to either geometric sequence formula or arithmetic sequence formula. To recall, all sequences are an ordered list of numbers. Example 1,4,7,10…. all of these are in a proper sequence. That is each subsequent number is increasing by 3. To make work much easier, sequence formula can be used to find out the last number (Of finite sequence with the last digit) of the series or any term of a series.
Formulas for Sequences
There are two types of sequence formula:
|Arithmetic Sequence Formula||an = a1 + (n − 1)d|
|Geometric Sequence Formula||an = a1 r(n − 1)|
a = first term
d = difference
n = a term which is to be found.
r = common ratio between two terms
Solved Examples Using Sequence Formulas
Question 1: What is the 10th term of the sequence 1, 3, 5, 7, 9…?
“n” here is 10
“a” is the first number = 1
Using the formula: an =a1 + (n−1)d
1 + (10 – 1) 2 = 1 + 9(2) = 19
Hence, the 10th term for the arithmetic sequence is 19.
Question 2: Find the 5th term of the geometric sequence 5, 10, 20, 40, ….?
Using the formula:
an = a1 r(n − 1)
Here, r = 2 [because, the ratio between two terms is 2 (i.e.,) 10/5 = 20/10 = 2 ]
an = 5 × 25−1 = 80
Hence, the 5th term for the geometric sequence is 80.