Find the 12^th term of a G.P. whose 8^th term is 192 and the common ratio is 2

Solution:

Let a be the first term of the G.P

It is given that common ratio, r = 2

Eighth term of the G.P, a₈ = 192

Therefore,

⇒ a₈ = ar^{8 - 1} = ar⁷

⇒ ar⁷ = 192

⇒ a (2)⁷ = 192

⇒ a (2)⁷ = (2)⁶ (3)

⇒ a = [(2)⁶ (3)]/(2)⁷ = 3/2

Hence,

a₁₂ = ar^{12 - 1}

= ar¹¹

= 3/2(2)¹¹

= (3)(2)¹⁰

a₁₂ = 3072

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 2

Find the 12^th term of a G.P whose 8^th term is 192 and the common ratio is 2

Summary:

We found out that the 12th term of a GP whose 8th term is 192 and whose common ratio is 2 is 3072