Question

if fourth term of an gp is 8and fifth term is 16 then what is the product of first 8 terms ​

Answer 1

Given : fourth term of a G.P. is 8 and fifth term is 16,  

To Find :  product of first  8 terms

Solution:

Let say  GP is

a , ar , ar² ,............................

fourth term of G.P  = ar³  = 8

fifth term of G.P  = ar⁴  = 16

=> ar⁴ /  ar³ = 16/8

=> r = 2

ar³  = 8

=> a(2)³ = 8

=> a = 1

first 8 terms of GP are

1 , 2¹ , 2²  , 2³ , 2⁴ ,  2⁵ , 2⁶  2⁷

Product = 1⁰ x 2¹ x 2²  x 2³ x 2⁴ x  2⁵ x 2⁶ x 2⁷

= 1 * 2¹⁺²⁺³⁺⁴⁺⁵⁺⁶⁺⁷

= 1 * 2²⁸

= 2²⁸

= 26,84,35,456

product of first  8 terms   = 2²⁸  = 26,84,35,456

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