Question

Please solve Q. 10.
Ans.=60+20/27.
Lesson GP

Answer 1

Hiii...

Now u can do it
.....

Answer 2

Q10.     Geometric Progression / Series.    To find the sum of numbers in GP.

  Series:  81, -27, 9, .... , -1/27

  Geom. Series:    a , a r , a r², a r³ , ..... , a r ⁿ⁻¹

  =>  a = 81.       r = (-27/81) = -1/3

        a r⁽ⁿ⁻¹⁾ = -1/27 
        =>  r⁽ⁿ⁻¹⁾ = -1/ [27 * 81]  = -1/[ 3³ * 3⁴ ]
                      = -1/3⁷ = (-1/3)⁽⁷⁾ 
                      = r⁷
              So  n - 1  = 7
                    n =  8.

       Sum =  a [ 1 - rⁿ ] / [ 1 - r ]
               =  81 [ 1 - (-1/3)⁸ ] / [ 1 - (-1/3) ]
               =  81 * (3⁸ - 1) / [ 3⁸ * 4 / 3 ]
               =  3⁴ * (3⁸ - 1) / ( 3⁷ * 4 )
               =  (3⁸ - 1)/108   = 1640/27
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Much simpler solution

we don't need to find n, as the last term is given.