Question

1, 5/4, 21/16,____what will be the nth term of the series?​

Answer 1

Given : 1, 5/4, 21/16

To Find : what will be the nth term of the series​

Solution:

1

5/4  = 1  + 1/4  =  1 + 1/2²   = 1  + 1/(2.1)²

21/16 = 5/4  + 1/16  = 5/4  + 1/4² = 5/4  + 1/(2,2)²

Hence

Tₙ  = Tₙ₋₁  +  (1/2n)²   where  T₁   = 1

T₂ = T₁  + (1/2(1))²  = 1 + 1/4 = 5/4

T₃ = T₂  + (1/2(2))²  =5/4 + 1/16= 21/16

Hence nth term of the series  Tₙ₋₁  +  (1/2n)²

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