→→Arithmetic sequence: When we talk about arithmetic sequence . there is a thing called Common Difference , which can be calculated by finding the difference between two consecutive terms, that is the beginning term and it's Succeeding term.
→n th term of Arithmetic sequence= A + (n-1) d, Here A= First term, d=Common Difference
If value of n changes ,that is for different positive integral values of n, we get different terms in a sequence.
→→→If we compare it with , linear function, which is represented as
→y= m x + c, here m= Slope of line, C= Y intercept
So, if slope of line changes , we get different equation of line.
→→When we talk about geometric sequence, the word comes into notion is Common ratio, which can be calculated by dividing the succeeding term by preceding term.
→→General formula for Geometric Sequence = [tex]a \times r^{n-1}[/tex], where a = First term , r= Common ratio
For, r> 1, each succeeding term increases by a fixed value called common ratio, and when r<1, each succeeding term is less than by it previous term by a fixed quantity, called common ratio.
→→Similarly, exponential function behaves in same way.
General formula for exponential functions = [tex]a \times b^{n}[/tex], or [tex]a \times b^{-n}[/tex] where a = Starting term
Keeping the value of b and ,a fixed, if n is positive , graph of the function is Strictly increasing,and if n is negative graph of function is strictly decreasing.
