Question

51-3
5) If for a sequence, t = 21-3 , show that the
sequence is a G.P.
Find its first term and the common ratio.​

Answer 1

Answer:

4/25 - First Term

5/2 - Common Ratio

Step-by-step explanation:

tn = 5ⁿ⁻³ / 2ⁿ⁻³

=> tn =  (5/2)ⁿ⁻³

t₁ = (5/2)¹⁻³  = (5/2)⁻²  = (2/5)²  = 4/25

t₂ = (5/2)²⁻³  = (5/2)⁻¹  = (2/5)¹  = 2/5

t₃ = (5/2)³⁻³  = (5/2)⁰  = 1

t₄ = (5/2)⁴⁻³  = (5/2)¹ = 5/2

t₅ = (5/2)⁵⁻³  = (5/2)² = 25/4

4/25  , 2/5  ,   1   , 5/2   ,  25/4  is the GP

first term = 4/25

Common Ratio = 5/2

Common Ration = tₙ₊₁/tₙ  = (5/2)ⁿ⁺¹⁻³/(5/2)ⁿ⁻³  = (5/2)ⁿ⁻²/(5/2)ⁿ⁻³  

= (5/2)(5/2)ⁿ⁻³ /(5/2)ⁿ⁻³

= 5/2

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