AP EAMCET2006MathematicsSequences and Series

1+ 2 4 + 2 5 4 8 + 2 5 8 4 8 12 + 2 5 8 11 4 8 12 16 + is equal to :

Options

A4^ -2 / 3
B[3] 16
C[3] 4
D4^ 3 / 2

Correct answer

B. [3] 16

Step-by-step solution

Let S=1+ 2 4 + 2 5 4 8 + 2 5 8 4 8 12 + On comparing with (1+x)^n=1+n x+ n(n-1) 2 ! x^2+ we get n x= 2 4 (i) and n(n-1) 2 ! x^2= 2 5 4 8 (ii) From (i) and (ii) n(n-1) 2 ! x^2 n^2 x^2 = 2 5 4 8 2 4 2 4 n-1 n = 5 2 2 n-2=5 n n=- 2 3 On Putting the value of n in Eq. (i), we get - 2 3 x= 2 4 x=- 3 4 S=(1+x)^n= (1- 3 4 )^ -2 / 3 = ( 1 4 )^ -2 / 3 = [3] 16

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