Question

Third term of a GP is 27 and its 6th term is 729, find the product of its first and seventh terms

Answer 1

3rd term 
ar^2 =27
a = (27/r^2)
6th term
ar^5 = 729
(27/r^2)(r^5)= 729         ( substitution)
(r^3) 27 = 729
r^3= 27
r= 3

using first equation
ar^2=27
a(9)=27
a=3
product of first and seventh terms:
first term = 3
7th term = 3 ( 3^6)
=729
first term X 7th term = 3 X 729
=2187  (FINAL ANSWER)
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