Question

Find the common ratio in a geometric sequence where the first term is 2/5 and the third term is 1/10

Answer 1

GP is given by = arⁿ⁻¹

First term of GP =  2/5,    a = 2/5      ......(i)

Third term = 1/10,             ar² = 1/10    ......(ii)

(ii) ÷ (i)

ar² ÷ a = (1/10) ÷ (2/5)

r²  =    1/10 × 5/2

r²  =  1/4            Take square root of both sides

r = √(1/4)

r = 1/2.

Common ratio = 1/2.