Articles

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

by Anil Satpute Mathematician, Writer, Poet
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. It is 100% FREE ]

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

For More details Please Click HERE.
Anil Baburao Satpute

Sponsor Ads


About Anil Satpute Advanced   Mathematician, Writer, Poet

85 connections, 0 recommendations, 293 honor points.
Joined APSense since, March 24th, 2013, From Mumbai, India.

Created on Dec 31st 1969 18:00. Viewed 0 times.

Comments

No comment, be the first to comment.
Please sign in before you comment.