Question

Find the 20th and n th terms of the G.P. \(\frac{5 }{ 2} ,\frac{ 5}{ 4} ,\frac{ 5 }{ 8} \),......

Answer 1

Given:

The given G.P. is:

5/2 , 5/4 , 5/8 , …

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Step 1: Identify first term and common ratio

First term,
a = 5/2

Common ratio,

r = (second term) / (first term)

r = (5/4) ÷ (5/2) = (5/4) × (2/5) = 1/2

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Step 2: Write the formula for the n^th term of a G.P.

T_n = a rⁿ⁻¹

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Step 3: Find the 20^th term

T₂₀ = (5/2) (1/2)¹⁹

T₂₀ = 5 / 2²⁰

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Step 4: Find the n^th term

T_n = (5/2) (1/2)ⁿ⁻¹

T_n = 5 / 2ⁿ

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Final Answers:

20^th term:
T₂₀ = 5 / 2²⁰

n^th term:
T_n = 5 / 2ⁿ