Sample Material of Online Coaching For SSC CGL (Tier - 2) - Sequence and Series


Sample Material SSC CGL TIER-2 Online Coaching


Numerical Aptitude (Chapter: Sequence and Series)

Arithmetic Progression(AP)

An arithmetic progression is a sequence in which terms increase or decrease by a constant number called the common difference.
(i) The sequence 2, 6, 10, 14, 18, 22… is an arithmetic progression whose first term is 2 and common difference 4.
(ii) The sequence …is an arithmetic progression whose first term is 2 and common
difference ½.
An arithmetic progression is represented by a,(a + d), (a + 2d), (a + 3d) ....... + (n – 1)d
Here, a = first term
d = common difference
n = number of terms in the progression

  • The general term of an arithmetic progression is given by Tn = a + (n – 1) d.
  •  The sum of n terms of an arithmetic progression is given by S, = [2a + (n – 1) d] or Sn = 2 [a + l]
    where l is the last term of arithmetic progression.
  •  If three numbers are in arithmetic progression, the middle number is called the arithmetic mean of the other two terms.
  •  If a, b, c are in arithmetic progression, then b = where b is the arithmetic mean.
  •  Similarly, if ‘n’ terms al, a2, a3… an are in AP, then the arithmetic mean of these ‘n’ terms is given by
    AM =
  •  If the same quantity is added or multiplied to each term of an AP, then the resulting series is also an AP.
  •  If three terms are in AP, then they can be taken as (a – d), a, (a + d).
  •  If four terms are in AP, then they can be taken as (a – 3d), (a – d), (a + d), (a + 3d).
  •  If five terms are in AP, then they can be taken as (a – 2d), (a – d), a, (a + d), (a + 2d).
     

Geometric Progression (GP)
 

A geometric progression is a sequence in which terms increase or decrease by a constant ratio called the common ratio.
(i) The sequence 1, 3, 9, 27, 81…is a geometric progression whose first term is 1 and common ratio 3.
(ii) The sequence is a geometric progression whose first term is 1 and common ratio
A geometric progression is represented by a, ar, ar2…arn–1.
Here, a = first term
r = common ratio
n = number of terms in the progression.

  •  The general term of a geometric progression is given by Tn = an–1
  •  The sum to n terms of a geometric progression is given by when r < 1 when r > 1
  •  If three numbers are in geometric progression, the middle number is called the geometric mean of the other two terms.
  •  If a, b, c are in geometric progression, then where b is the geometric mean.
  •  Similarly, if n terms a1, a2, a3, a4,…an are in geometric progression, then the geometric mean of these n terms is given by GM =
  •  For a decreasing geometric progression the sum to infinite number of terms is where a = first term and | r | < 1.
  •  If every term of a GP is multiplied by a fixed real number, then the resulting series is also a GP.
  •  If every term of a GP is raised to the same power, then the resulting series is also a GP.
  •  The reciprocals of the terms of a GP is also a GP.
  •  If three numbers are in GP, then they can be taken as a, ar.
  •  If four numbers are in GP, then they can be taken as
  •  If five numbers are in GP, then they can be taken as

Harmonic Progression (HP)

If the reciprocals of the terms of a series form an arithmetic progression, then the series is called a harmonic progression.
(i) The sequence is a harmonic progression as is in arithmetic progression.

  •  If a, b, c are in harmonic progression, then b = where b is the harmonic mean.

:: Home Assignment for Practice ::

1. If five times the fifth term of an AP is equal to seven times, the seventh term of the AP, then what is the twelfth term?

(a) –1
(b) 0
(c) 1
(d) –2

2. Three terms are in AP such that their sum is 18. The sum of the first two terms is six more than the sum of the last two terms. Find the last term.

(a) 6
(b) 9
(c) 3
(d) 2

3. Determine k, so that (k + 2), (4k – 6) and (3k – 2) are three consecutive terms of an AP.

(a) 3
(b) 2
(c) 4
(d) 6

4. In an AP, the first term is 2 and the sum of the first five terms is one-fourth the sum of the next five terms. Find the second term.

(a) –4
(b) –10
(c) –16
(d) –12

5. The sum of four terms in an AP is 64. The product of the extreme terms is 220. Find the first and fourth term.

(a) 14, 28
(b) 10, 22
(c) 28, 14
(d) 6, 30

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