Arithmetic Progression(AP)
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d".
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d ,......................, a + (n-1)d.
where a is first term , d is the common difference
example : 2,4,6,8..........20
d= T2 - T1
Tn = a+(n-1)d
Sn = (2a + (n-1)d)
Sn = n(a*l)/2
where l is the value of the last term
Geometric Progression(GP)
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio. For example, the sequence 4, -2, 1, - 1/2,.... is a Geometric Progression (GP) for which - 1/2 is the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on.
Where a is the first term , r is common ration (Tn / Tn-1)
Tn = arn-1
Sum of geometric series
\[S_{n} = \frac{a\left ( r^{n} -1\right )}{r-1} \] is r > 1
\[S_{n} =\frac{a\left ( 1 - r^{n} \right )}{1-r} \] if r<1
for infinite series
\[S_{n} =\frac{a}{1-r} \]
