In a geometric sequence 10th is 12 and 20th element is 512 F

In a geometric sequence 10th is 1/2 and 20th element is 512. Find first element and common ratio.

Solution

Let the geometric series be a ,ar² ,a r³ , ------

10 th term = t ₁₀ = a r⁹ = 1/2 ------(1)

20 th term = t₂₀  = a r ¹⁹ = 512  -----(2)

divide eq (2) by divide (1)

t₂₀  / t₁₀  = 512 x2 = r¹⁰ => r=2 substituting in eqn (1)

a = 1 /1024, r = 2