The third term of a G.P is 10. Then the product of first five terms is *
1000
10000
100
100000
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Given : The third term of a G.P is 10
To Find : the product of first five terms
Solution:
Let say GP is
a/r² ,a/r , a , ar , ar²
a = 10
product of first five terms = ( a/r²) * (a/r )* a * ar * ar²
= a⁵
= 10⁵
= 100000
the product of first five terms is 100000 if third term of a G.P is 10
Another way GP is
a , ar , ar² , ar³ , ar⁴
a = 1st term
r = common ratio
3rd term ar² = 10
product of first five terms = a * ar * ar² * ar³ * ar⁴
=a⁵.r¹⁺²⁺³⁺⁴
= a⁵.r¹⁰
= a⁵(.r²)⁵
= (ar²)⁵
= 10⁵
= 100000
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