Question

the 6th and the 13th terms of a GP are 64 and 8192 respectively. Find the 10th term of the GP
plzzz answer this as fast as possible
coz kl mera exam hai!!!!!!!

Answer 1

Answer:

1024

Step-by-step explanation:

(i) 6th term of GP is 64.

⇒ a₆ = 64

⇒ ar⁶⁻¹ = 64

⇒ ar⁵ = 64  

(ii) 13th term of GP is 8192.

⇒ ar¹³⁻¹ = 8192

⇒ ar¹² = 8192

On dividing (ii) by (i), we get

⇒ (ar¹²)/(ar⁵) = (8192/64)

⇒ r⁷ = 128

⇒ r⁷ = 2⁷

⇒ r = 2

Substitute r = 2 in (i), we get

⇒ ar⁵ = 64

⇒ a(2)⁵ = 64

⇒ a = 64/32

⇒ a = 2

Thus, a = 2 & r = 2.

We use the formula:

a(n) = arⁿ⁻¹

10th term of the GP:

a ₁₀ = ar¹⁰⁻¹

     = ar⁹

     = 2(2)⁹

     = 1024

Therefore, 10th term of GP is 1024.

Hope it helps!

Answer 2

Here a6 is the 6th term, a13 is the 13th term and a10 is the 10th term

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