Monday, May 6, 2013

59-09 Basics of Arithmetic & Geometric Progression (Grades 9 to 12) Part-09

Blog-59

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.

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Following two files are very important to improve your base for remembering the formulas. It is 100 % free for all the students of the world. Download these two files, take the Print Out of these files on two sides of the paper and practice these formulas for your benefit to get high scores in Mathematics Standard 10/ Grade 10.

1) Algebra Formulas
2) Geometry Formulas


Note: 
1) To find three consecutive terms in GP, consider the terms as (a/r),  (a), (ar).
2) To find four consecutive terms in GP, consider the terms as (a/r3),  (a/r), (ar), (ar3).
3) To find five consecutive terms in GP, consider the terms as (a/r2),  (a/r), (a), (ar), (ar2).

A) Find three consecutive three terms in GP if  the sum of first & third term is 35 and the product of all the three terms is 2744.

Solution:
1) Let " a " be the first term and " r " be the common ratio of GP.
2) Let three consecutive terms in GP be  (a/r),  (a), (ar).
3) According to the problem, 
                 (a/r) (a)(ar) = 2744
                             (a3) = 4 x 686
                             (a3) = 4 x 2 x 343
                             (a3) = 4 x 2 x 7 x 49
                             (a3) = (2 x 7)3
                               (a) = (2 x 7)
                               (a) = (14)
4) Simillarly,
                        a/r + ar = 35
                     a (1/r + r) = 35
                   14 (1/r + r) = 35
                        (1/r + r) = 35/14
                        (1/r + r) = 5/2
                        (1/r + r) = 2 + 1/2
5) This shows that r = 2 or 1/2
6) Answer: Taking r = 2 and a = 14, the three consecutive terms are 7, 14 and 28.
                    Taking r = 1/2 and a = 14, the three consecutive terms are 28, 14 and 7.

Note:
1) Arithmetic Mean: The three terms p, q and r in AP gives " q " as the arithmetic mean between p and q. So,
                 q - p = r - q
                 q + q = r + p
                    2 q = r + p
                       q = (r + p) / 2
2) Geometric Mean: The three terms p, q and r in GP gives " q " as the geometric mean between p and r. So,
                 q / p = r / q
                 q x q = r x p
                     q2 = r x p
                       q = (r p)1/2
Some Important Problems on AP & GP

A) In an AP  6, 12, 18, ....., how many terms shows the sum as 7650.

Solution:
1)   Here, a = 6, d = 6 and Sn = 7650.
2)   We know that 

        






















3) Answer: Total number of term in AP having sum as 7650 is 50.

Anil Satpute