Geometric Sequence Worksheet Solution3





In the page geometric sequence worksheet solution3 you are going to see solution of each questions from the geometric series worksheet.

(6) If the geometric sequences 162,54,18,......... and 2/81,2/27,2/9,.......... have their nth term equal,find the value of n.

Solution:

Since nth term of the given geometric sequence are equal let us find nth term of the given sequences one by one.

    162,54,18,.........

a = 162   r = 54/162

             r = 1/3

     2/81,2/27,2/9,..........

a = 2/81    r = (2/27)/ (2/81)

                  = 2/27 x 81/2

               r = 3

t n = a r^(n-1)

     = 162 (1/3)^(n-1)

     = 162 (3⁻¹)^(n-1)

     = 162 (3⁻ⁿ⁺¹)  ------ (1)

t n = a r^(n-1)

     = (2/81) x (3)^(n-1)  ------ (2)

t n = t n 

162 (3⁻ⁿ⁺¹) = (2/81) x (3)^(n-1)

[(162 x 81)/2] (3⁻ⁿ⁺¹) = (3)^(n-1)

(81 x 81)(3⁻ⁿ⁺¹) = (3)^(n-1)

(3⁴ x 3⁴)(3⁻ⁿ⁺¹) = (3)^(n-1)

(3⁸)(3⁻ⁿ⁺¹) = (3)^(n-1)

(3)⁻ⁿ ⁺ ⁹ = (3)^(n-1)

   - n + 9 = n - 1

  - n - n = -1 - 9

     -2 n = -10

         n = 10/2

         n = 5  

from this we can decide 5th term of those sequence are equal.


(7) The fifth term of a G.P is 1875.If the first term is 3,find the common ratio.

Solution:

 Fifth term = 1875

 First term = 3

 t₅ = 1875

  a = 3

 a r⁴ = 1875

 3 r⁴ = 1875

   r⁴ = 1875/3

   r⁴ = 625

   r⁴ = 5⁴

   r = 5

Therefore the common ratio is 5.


(8) The sum of three terms of a geometric sequence is 39/10 and their product is 1. Find the common ratio and the terms.

Solution:

Let the first three terms are a/r,a,ar

Sum of three terms = 39/10

Product of three terms = 1

(a/r) + a + a r = 39/10   ------ (1)

(a/r) x a x a r = 1

        a³ = 1³

        a = 1

Substitute a = 1 in the first equation

(1/r) + 1 + 1 r = 39/10

 (1 + r + r²)/r = 39/10

  10(1 + r + r²) = 39 r

  10 r² + 10 r - 39 r + 10 = 0

  10 r² - 29 r + 10 = 0

  (2r - 5) (5r - 2) = 0

  2 r - 5 = 0          5r - 2 = 0

    2 r = 5                5 r = 2

       r = 5/2                r = 2/5

a/r = 1/(5/2)                                 a/r = 1/(2/5)

     = 2/5                                           = 5/2

 a = 1                                            a = 1  

ar = 1(5/2)                                    ar = 1(2/5)  

   = 5/2                                             = 2/5

Therefore the three terms are (2/5),1,(5/2) or (5/2),1,(2/5)



you can get solution for remaining question in the next page.geometric sequence worksheet solution3 geometric sequence worksheet solution3