Question

find the 12th term of G.P whose 8th term is 192 &the common ratio is 2​

Answer 1

Answer:

Given; Common ratio = 2, 8th term = 192

Let a be the 1st term of the G.P.

We know that,

a(n) = ar⁽ⁿ⁻¹⁾

where a(n) = nth term of G.P.

n = number of terms

a = first term

r = common ratio

a₈ = ar⁽⁸⁻¹⁾

a₈ = ar⁷

ar⁷ = 192

a(2)⁷ = 192

a(2)⁷ = (2)⁶ (3)

⇒ a = {(2)⁶ (3)}/(2)⁷

⇒ a = {(3)/(2)⁷⁻⁶}

⇒ a = (3)/(2)¹

⇒ a = 3/2  (first term)

So,

n₁₂ = ar⁽¹²⁻¹⁾

n₁₂ = 3/2 × 2⁽¹²⁻¹⁾

n₁₂ = 3/2 × 2⁽¹¹⁾

n₁₂ = {3 × (2)⁽¹¹⁻¹⁾}

n₁₂ = 3 × 2⁽¹⁰⁾

n₁₂ = 3 × 1024

n₁₂ = 3072

Answer.

Step-by-step explanation: