The first two terms of a G.P. are 125 and 25 respectively. Find the 5^th and the 6^th terms of the G.P.

Given,

⇒ a = 125

⇒ a₂ = 25

⇒ ar = 25

⇒ 125r = 25

⇒ r = $\dfrac{25}{125} = \dfrac{1}{5}$.

a₅ = ar⁴

= $125 \times \Big(\dfrac{1}{5}\Big)^4$

= $125 \times \dfrac{1}{625}$

= $\dfrac{1}{5}.$

a₆ = ar⁵

= $125 \times \Big(\dfrac{1}{5}\Big)^5$

= $125 \times \dfrac{1}{3125}$

= $\dfrac{1}{25}.$

Hence, $a$5 = \dfrac{1}{5} \text{ and } a6 = \dfrac{1}{25}.