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| Number System (Part 3 of 5) |
PROGRESSION
This topic covers the concepts of AP and GP and their formulas to solve the questions related to the Progression !!
A succession of numbers formed and arranged in a definite order according to certain definite rule, is called a progression.
1. Arithmetic Progression (A.P.)
If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P.
An A.P. with first term a and common difference d is given by a, (a + d), (a + 2d), (a + 3d) …
The nth term of this A.P. is given by Tn =a (n - 1) d.
The sum of n terms of this A.P. Sn = n/2 [2a + (n - 1) d] = n/2 (first term + last term)
2. Geometrical Progression (G.P.)
A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression. The constant ratio is called the common ratio of the G.P. A G.P. with first term a and common ratio r is... a, ar, ar2
In this G.P. Tn = arn-1 and Sn = a(1-rn) / (1-r)
1. Arithmetic Progression (A.P.)
If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P.
An A.P. with first term a and common difference d is given by a, (a + d), (a + 2d), (a + 3d) …
The nth term of this A.P. is given by Tn =a (n - 1) d.
The sum of n terms of this A.P. Sn = n/2 [2a + (n - 1) d] = n/2 (first term + last term)
2. Geometrical Progression (G.P.)
A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression. The constant ratio is called the common ratio of the G.P. A G.P. with first term a and common ratio r is... a, ar, ar2
In this G.P. Tn = arn-1 and Sn = a(1-rn) / (1-r)
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