**Progressions**

**Sequence**

A succession of numbers formed and arranged in a definite order according to a certain definite rule is called a sequence.

**Arithmetic Progression (A.P.)**

It is a sequence in which each term, except the first one differs the preceding term by a constant. This constant is called the common difference. We denote the first term by a, common difference by d, nth term by Tṇ and the sum of first n terms by Sṇ.

**Examples**

5, 8,11,14,17...is an A.P. in which a=5 and d = (8-5) =3. 8, 5, 2,-1,-4,-7.... is an A.P. in which a = 8 and d = (5-8) = -3.

**General Term of an A.P.**

In a given A.P., let first term =a, common difference =d. Then,

Tn= a + (n-1) d. Sum of n terms of an A.P. Sn = n/2[2a+ (n-1) d] Sn = n/2 (a + L), where L is the last term.

**Geometrical Progression (G.P.)**

A sequence in which each term, except the first one bears a constant ratio with its preceding term, is called a geometrical progression, written as G.P. The constant ratio is called the common ratio of the G.P. We denote its first term by a and common ratio by r.

**Example**

2, 6, 18, 54, is a G.P.in which a=2 and r=6/2=3. 24, 12, 6, 3... Is a G.P. in which a = 24 and r = 12/24=1/2.

General Term of a G.P.: In a G.P. we have

Tn= ar^{n-1}Sum of n terms of a G.P. Sn = a (1-r^{n})/ (1-r), When r < 1 a (r - 1^{n})/(r-1), When r > 1

**Arithmetic Mean**

A.M. of a and b = 1/2(a+b).

**Geometric Mean**

G.M. of a and b =√ab

**Some General Series**

(i) 1+2+3+4+…….+n=1/2n (n+1).

(ii) 1^{2}+2^{2}+3^{2}+4^{2}+……+n^{2} = n(n+1)(2n+1)/6

(iii) 1^{3}+2^{3}+3^{3}+4^{3}+…..+n^{3}= {1/2 n(n+1)}^{2
}

**Progressions Online Test – Progressions Quiz Details**

Online Test Name |
Progressions |

Exam Type |
Chapter & Multiple Choice Questions |

Category |
Aptitude Quiz |

Number of Questions |
25 |

CAT Algebra question from Progressions that appears in the Quantitative Aptitude section of the CAT Exam consists of concepts from Number Theory and Algebra. It involves concepts based on Artihmetic Progressions and Geometric Progressions. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with the following questions. In CAT Exam, one can generally expect to get 1~2 questions from Progressions. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free