ARTHIMETIC PROGRESSION (समांतर श्रेणी) CONCEPT AND IMPORTANT QUESTION FOR NDA MATHEMATICS 2022 | HELP4NDA

 ARTHIMETIC PROGRESSION (समांतर श्रेणी)

PROGRESSION :- sequence following in a certain pattern is called Progression.

ARTHIMETIC PROGRESSION :- common difference is same in this sequence.

    Eg.   1, 3,5, 7,_ _  _  _ _ ,  T_n^th

COMMON DIFFERENCE :   3-1 = 5-3=2

(C D = difference of two consecutive no.)

T_n^th  = a + (n-1) d

GENERAL TERM :- a , a+d , a+2d , ……………… , a+(n-1)d

SUM OF N ^th   TERM OF AP :- S_N  = n/2{2a+(n-1)d}

                                                   S_N = n/2{ a+l}

PROPERTIES :-

1.   1.  If a constant term is added or subtracted from each term of an AP , then the resulting sequence is also in AP.

Eg.  1,3,5,7      (d=2)

        1+2, 3+2 ,5+2 ,7+2

        3 , 5 ,7 ,9    (also in AP)   

        (d=2)

 

2.    2.  If each term of an AP is multiplied  or divided by a non-zero constant K , then also the resulting sequence in AP.

   Eg.   a , b, c               in AP

            ka , kb ,kc    in AP

           a/k , b/k ,c/k  in AP .

3.     Selection of no. in AP.

·       3 numbers   :-   a-d ,a ,a+d

·       4 numbers  :-   a-3d ,a-d , a+d ,a+3d

·       5 numbers   :-  a-2d ,a-d ,a ,a+d ,a+2d

4.    3.  T_n^th = S_N – S_N-1

5.   4.  If   T_n = pn+q

D = p

1^st  term = p+q

Eg.  5p-3

 D= 5

      1^st  term = 5-3=2

6.   5.  If S_N = An²+ Bn

Then d= 2A

Eg.  S_n = 5n²+ 4n

     D = 10

7.     6. If the p^th  term of an AP is q and the q^th term of an AP is p , then its (p+q)^th term is 0 and the n^thterm = p+q-r

T_P= q

T_q  = p    ,       T_P+Q = 0

T_n^th= p+q-n

8.    7.  If in  an AP

S_P= q

S_q= p

Then , S_p+q= -(p+q)

Eg.  S₁₀ = 15 , S₁₅ = 10

THEN S₂₅= -(15+10) = -25

9.     8. Ratio of sum of m terms and n terms is  m²: n² , then the ratio of m^th and n^th term is :

          2m-1/2n-1

 

ARTHIMETIC MEAN :-

Let a and b be two quantities , then A M b/w a and b ,

           AM = a+b/2

Ø  Sum of all AM’s b/w a and b

A1+A2+A3+A4+A5+………………………+A_N  =  n(a+b/2)

 

 PRACTICE QUESTION ON A.P :-

1. Let Sn denotes the sum of n terms of an AP, whose first term is a. If the common difference d=Sn−kSn−1+Sn−2, then k is equal to
(a)   3
(b)  2
(c)  5
(d)  7


2. Find the sum of all numbers between 200 and 400 which are divisible by 7.

(a)    8729
(b)   8728
(c)   9729
(d)   8792

 3. What is the fourth term of an AP of n terms whose sum is n(n + 1)? 

      A  6        B 8        C 12       D 20

 

 4. Let Tr be the rth term of an AP for r = 1,2,3, …….. If for some distinct positive integers m and n we have Tm = 1/n and Tn = 1/m, then what is Tmn equal to ?

 

 A  1        B (mn)-1            C  m-1 + nn-1          D 0

 

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