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The common ratio , the last term , and the sum of G.P. is 3, 486 and 728. Find first and the number of terms.

The common ratio , the last term , and the sum of G.P. is 3, 486 and 728. Find first and the number of terms.

Grade:Upto college level

3 Answers

vikas askiitian expert
509 Points
10 years ago

r = 3 , last term = 486  ,  sum = 728

last term = arn-1 = 486    ..................1

sum = a(rn - 1)/r-1 = 728     ................2

 

divide both

 

728/486 = (rn-1)/[(r-1)(rn-1)

r = 3 so

728/486 = 3n-1/2x3n-1 

729 - 1 / 243 = 3n - 1 /3n-1

36 - 1 / 35  =  3n - 1 / 3n-1

comparing both sides we get

n = 6 or n-1 = 5

total terms = 6

from eq 1 , arn-1 = 486

  a 35 = 486 = 243x2 = 35x2

 a = 2

 

firat term is 2 & total terms are 6 ,

 

approve if u like my ans

 

Sudheesh Singanamalla
114 Points
10 years ago

1043_16302_GP.jpg

 

Please approve

anitha ashok
16 Points
10 years ago

Hello Sir,

Please give me the answer for this question from Arithmetic Progression.

Insert a A.M. between 5 and 20.

Anitha.

 

 

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