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

r = 3 , last term = 486  ,  sum = 728

last term = ar^n-1 = 486    ..................1

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

divide both

728/486 = (rⁿ-1)/[(r-1)(r^n-1)

r = 3 so

728/486 = 3ⁿ-1/2x3^n-1 

729 - 1 / 243 = 3ⁿ - 1 /3^n-1

3⁶ - 1 / 3⁵  =  3ⁿ - 1 / 3^n-1

comparing both sides we get

n = 6 or n-1 = 5

total terms = 6

from eq 1 , ar^n-1 = 486

  a 3⁵ = 486 = 243x2 = 3⁵x2

 a = 2

firat term is 2 & total terms are 6 ,

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Hello Sir,

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

Insert a A.M. between 5 and 20.

Anitha.