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Sequence Formula

All sequences is 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 our work much easier, sequence formula can be used to find out the last number (Of finite sequence with a last digit) of the series or any term of a series.

There are two types of sequence formula:

  1. Arithmetic
  2. Geometric

Arithmetic Sequence Formula:

\[\LARGE a_{n}=a_{1}+(n-1)d\]

Geometric Sequence Formula:

\[\LARGE g_{n}=g_{1}r^{(n-1)}\]

Solved Examples

Question 1: What is the 10$^{th}$ term of the sequence  1, 3, 5, 7, 9…?

Solution:

Given,
n here is 10
a is the first number = 1

Using the formula: $a_{n}=a_{1}+(n-1)d$

1 + (10-1) 2 = 19

Hence the 10$^{th}$ term for the sequence is 19.

Question 2: Find the 5th term of the geometric sequence 5, 10,20, 40, ….?

Solution:

Using the formula:

$g_{n}=g_{1}r^{(n-1)}$

$g_{n}=5\times 2^{5-1}=80$