Question

can you please tell me all the formulae of AP and GP in maths

Answer 1

Ap =
a=a+b divided by 2


Gp =

b=root AC

Answer 2

An arithmetic progression is given by a, (a + d), (a + 2d), (a + 3d), ... 
where a = the first term , d = the common difference
nth term of an arithmetic progression

tn = a + (n – 1)d 

where tn = nth term, a= the first term , d= common differen

Number of terms of an arithmetic progression

n=(l−a)d+1n=(l−a)d+1

where n = number of terms, a= the first term , l = last term, d= common difference
Sum of first n terms in an arithmetic progression

Sn=n2[ 2a+(n−1)d ] =n2(a+l)Sn=n2[ 2a+(n−1)d ] =n2(a+l)

where a = the first term,
d= common difference,
l = tn = nth term = a + (n-1)d

Arithmetic Mean

If a, b, c are in AP, b is the Arithmetic Mean (AM) between a and c. In this case, b=12(a+c)b=12(a+c)

The Arithmetic Mean (AM) between two numbers a and b = 12(a+b)12(a+b)

geometric progression(GP)
A geometric progression(GP) is given by a, ar, ar2, ar3, ... 
where a = the first term , r = the common ratio.
nth term of a geometric progression(GP)

tn=arn−1tn=arn−1 

where tn = nth term, a= the first term , r = common ratio, n = number of terms