### Arithmetic and geometric sequences and their summations - (7.1-7.3)

#### Understand the concept and the properties of arithmetic sequences

• An Arithmetic Sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For example, 4, 7, 10, 13, .....
We notice numbers above show predictable patterns. Each sucessive number is greater than the previous one by 3. Hence, it is an arithmetic Sequence
To find out the $$n^{th}$$ term of an Arithmetic Sequence, the general term of is given by $$T_n=a+(n-1)d$$,
• where $$T_n$$ is the $$n^{th}$$ term of the sequence,
• a is the first term of the sequence
• n denote the number of term
• d denote the common difference
Referring to examples above,
a is the first term of the sequnence, which is 4
d is the common difference, which is 3
13 is the fourth term of the sequence, $$\therefore n=4, T_4=13$$
• If the $$9^{th}$$ term and the $$11^{th}$$ term of an Arithmetic Sequence is 52 and 22. Find the first term and common difference of the Sequence.