what is arthimetic progression and geometric progression.?

Answer 1

Terms in an arithmetic progression share a common difference. For example, 1, 4, 7, 10, 13... is an arithmetic progression because consecutive terms differ by 3. (4-1=3, 7-4=3, 10-7=3, ...)
The general term of an arithmetic progression is a_n = a_1 + (n-1)d, where d is the common difference.

Terms in a geometric progression are in a common ratio. For example, 2, 6, 18, 54, 162,... is a geometric progression because consecutive terms are in ratio 1:3 (2x3=6, 6x3=18, 18x3=54, 54x3=162,...)
The general term of a geometric progression is a_n = a_1(r^(n-1)), where r is the common ratio.

Answer 2

In mathematics, an arithmetic progression or arithmetic sequence is a sequence(well define order) of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference 2.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

a(nth)=a1 +(n-1)*d

And a geometric progression (also known as a geometric sequence, and, inaccurately, as a geometric series) is a sequence of numbers such that the quotient of any two successive members of the sequence is constant. This ratio is called the common ratio of the sequence.

Thus without loss of generality a geometric sequence can be written as

a,ar,ar2,ar3,ar4,...
where r ≠ 0 is the common ratio and a is a scale factor. Thus the common ratio gives a family of geometric sequences whose starting value is determined by the scale factor. Pedantically speaking, the case r = 0 ought to be excluded, since the common ratio is not even defined; but the sequence that is always 0 is included, by convention

Answer 3

Terms in an arithmetic progression share a common difference. For example, 1, 4, 7, 10, 13... is an arithmetic progression because consecutive terms differ by 3. (4-1=3, 7-4=3, 10-7=3, ...)
The general term of an arithmetic progression is a_n = a_1 + (n-1)d, where d is the common difference.

Terms in a geometric progression are in a common ratio. For example, 2, 6, 18, 54, 162,... is a geometric progression because consecutive terms are in ratio 1:3 (2x3=6, 6x3=18, 18x3=54, 54x3=162,...)
The general term of a geometric progression is a_n = a_1(r^(n-1)), where r is the common ratio.

Answer 4

In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference 2.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

a(nth)=a(1)+(n-1)d

and in general

a(nth)=a(m)+(m-1)d

There is a lot more at the following source.

Answer 5

arithmetic progression is a series of no with common difference.like 1 3 5 7 9... cd is 2.gp is a series with common ratio like 2 6 18 54 ...ratio r =3

Answer 6

The sum of a sequence of number is AP (Arithmetic Progression) whereas the product would be the geometric progression (GP)

1+2+3+4+5+6.... (AP)
1*2*3*4*5*6*..... (GP)

Answer 7

Arithmetic progression: a, a+d, a+2d, a+3d,...
If a is the first term, d the common difference, n the number of terms, l the lst term, and s the sum of n terms, then
l = a+(n-1)d, s = (n/2)(a+l)
The arithmetic mean of a and b is (a=b)/2

Geometric progression: a, ar, ar62, ar^3,...
If a is the first term, r the common ratio, n the number of terms, l the last term, and Sn the sum of n terms, then
l=ar^(n-1)
Sn = a[(r^n-1)/(r-1)] = (rl-a)/(r-1)
If r^2<1, Sn approaches the limit Sinfinigy as n increases without limit,
Sinfinity = a/(1-r)
The geometric mean of a and b is sqr(ab)

Answer 8

Arithmetic progression is a series of no. where the difference of two sequel numbers are equal.
For Example: 1,5,9,13,17,...
In this Example (5-1)=(9-5)=(13-9)=(17-13)....=4
Geometric progression is also a series of No.where the ratio of two sequel
number are equal.
For example: 1,2,4,8,16,32,....
In this example (2/1)=(4/2)=(8/4)=(16/8)=(32/16).....=2
if there is three No. in A.P.
are a,b,c then Arit.mean(b)=(a+c)/2
if there is three No. in G.P.
are a,b,c then Geome.mean(b)=squrt of (a*c)

Answer 9

arithmetic progression or AP means the two consecutive nos. in a series vary by a constant term.
For eg:2,6,10.....2(n-1)
6-2=4 again10-6=4.

Answer 10

A.P is a series of numbers which progresses by addition of a common number e.g.1 3 5 7 9 .............when the first no.is added by a common no. i.e.2.but G.P is a series of numbers which progresses by multiplication of a common no. whose power increases from one onwards.
formula: nth term= a(1-r raised to the power n)/(1-r)
where a is the first no.
r is the common difference
and n is the term