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  • Aptitude – Progression – Mathematics Notes – For W.B.C.S. Examination.
    Posted on May 20th, 2019 in Mathematics
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    Aptitude – Progression – Mathematics Notes – For W.B.C.S. Examination.

    Sequence

    A succession of numbers formed and arranged in a definite order according to a certain definite rule is called a sequence.Continue Reading Aptitude – Progression – Mathematics Notes – For W.B.C.S. Examination.

    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= arn-1
    Sum of n terms of a G.P.
    Sn = a (1-rn)/ (1-r), When r < 1
    a (r - 1n)/(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) 12+22+32+42+……+n2 = n(n+1)(2n+1)/6 
    (iii)  13+23+33+43+…..+n3= {1/2 n(n+1)}2
    
    

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