Saturday, April 20, 2013

02 Basics of Arithmetic & Geometric Progression (Grades 9 to 12) Part-02

Blog-61


Dear Students,


Download following files for learning Formulas more effectively. Take the print out of these files and write your answers daily to improve your scores in 10th standard/grade.


[ Note: The following 2 files are available in the secured drive. While downloading, your email might be asked. Please provide it to download the files. I assure that your email-id will not be given to anybody ]

1) Algebra Formulas
2) Geometry Formulas


In the Previous Blog we had seen some important concepts of Arithmetic & Geometric Progression. Click HERE to Revise that Blog.


In this Blog, we Describe the Important Formulas of an AP & GP.
1) tn =  a + (n - 1) d 
2) Sn = n * (a + l)/2
3) Sn = n * [ 2 a + (n - 1) d ) ] / 2

Now we will see some examples:

Problems related to tn =  a + (n - 1) d:

A) Find nth term of an AP 3, 5, 7, 9 ...


Solution:
1)  Here a = 3, d = (5 - 3) = 2 so, d = 2.
2)  We know that 
      tn =  a + (n -1) d
          =  3 + (n -1) (2)
          =  3 + (2 n - 2)
          =  1 + (2 n)
          =  (2 n) + 1
3) Answer: Here the nth term of an AP is  tn =  (2 n) + 1 

B) Find first term of an AP in which d = 4 and it's 100th term is 403.


Solution:
1)  Here d = 4 and t100 =  403.
2)  We know that 
      tn =  a + (n -1) d
   403 =  a + (100 - 1)*(4)
   403 =  a + (99)*(4)
   403 =  a + (396)
       a =  403 - 396
       a =  7
3) Answer: Here the 1st term is a = 7

C) If  nth term of an AP is m and mth term of an AP is n, then find the value of d.


Solution:
1)  Let " a " be the 1st term and " d " be the common difference.
2)  We know that 
      tn =  a + (n -1) d
3)  So we,
      t =  a +  (n -1) d = m      ----------- (1)
      tm =  a + (m -1) d = n       ----------- (2)
               Subtract equation (2) from (1) we get,
        a +  (n -1) d = m
        a + (m -1) d =  n  
     (-)  (-)               (-)  
----------------------------------
(n - 1 - m + 1) * d = (m - n)
           (n - m) * d = (m - n)
                         d = (m - n)/(n-m)
                         d = - 1
4) Answer: Here common difference is d = - 1

Few more problems will be published in the next Blog.

Anil Satpute