Question

5th and 13 th term of a go are 32 and 8192 find the 10 th tetm

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Answer 1

Solution :-

6th term of GP is 64

⇒ a₆ = 64

⇒ ar⁶⁻¹ = 64

⇒ ar⁵ = 64 ........ ( i )

13th term of GP is 8192

⇒ ar¹³⁻¹ = 8192

⇒ ar¹² = 8192 ........ ( ii )

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

We use the formula:

Tₙ = arⁿ⁻¹

10th term of the GP:

⇒ T₁₀ = ar¹⁰⁻¹

⇒ T₁₀ = ar⁹

⇒ T₁₀ = 2(2)⁹

⇒ T₁₀ = 1024

10th term of GP is 1024

Answer 2

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