If second term of a G.P. is 2 and the sum of its infinite terms is 8,

1.	If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term isA. 1/4B. 1/2C. 2D. 4
Answer» Let the GP be a,ar,ar² Sum of infinite terms is given by ⇒ s_∞ = a/1-r ⇒ 8 = a/1-r ⇒ Also according to the question ar = 2 ∴ r = 2/a ∴ Substituting in above equation ⇒ 8 = \(\cfrac{a}{1-\frac{2}{a}}\) ⇒ 8(a - 2) = a² ⇒ a² - 8a+16 = 0 ⇒ (a - 4)² = 0 ⇒ a = 4.

If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term isA. 1/4B. 1/2C. 2D. 4

Answer»

Let the GP be a,ar,ar²

Sum of infinite terms is given by

⇒ s_∞ = a/1-r

⇒ 8 = a/1-r

⇒ Also according to the question ar = 2

∴ r = 2/a

∴ Substituting in above equation

⇒ 8 = \(\cfrac{a}{1-\frac{2}{a}}\)

⇒ 8(a - 2) = a²

⇒ a² - 8a+16 = 0

⇒ (a - 4)² = 0

⇒ a = 4.