Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

For 0 < x < / 2 if x,( x+1) and 6( x+1) are in G.P., then:

Options

  1. Acommon ratio is 3 2
  2. Bcommon ratio is 1 / 2
  3. Cfifth term =162
  4. DS_n=1-(1 / 2)^n

Correct answer

C. fifth term =162

Step-by-step solution

aligned & 2( x+1)^2= x(6)( x+1) & 2 ^2 x+4 x+2=6 ^2 x+6 x & 4 ^2 x+2 x-2=0 & 2 ^2 x+ x-1=0 & (2 x-1)( x+1)=0 & x= 1 2 ; x=-1 (rejected) & x= 6 & G.P. 1 2 , 2 ( 1 2 +1 ), 6 ( 1 2 +1 ), & 1 2 , 3 2 , 9, & T₅=a r^4= 1 2 (3 2 )^4=81 2=162 & S_n= 1 2 [(3 2 )^n-1 ] 3 2 -1 & aligned

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Let = 3+4+8+9+13+14+ upto 40 terms. If ( )^ 1020 is a root of the equation x^2+x-2=0 , (0, 2 ) , then ^2 + 3 ^2 is equal to: 2026The sum 1 + 1 2 (1^2 + 2^2) + 1 3 (1^2 + 2^2 + 3^2) + upto 10 terms is equal to : 2026The value of 1^3 - 2^3 + 3^3 - + 15^3 is: 2026The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8 . If the first term of the A.P. is equal to the common ratio of the G.P. and the 2026For the functions f( ) = ^2 + ^2 , and g( ) = ^2 + ^2 , > > 0 , let _ 0 < < /2 f( ) = _ 0 < < g( ) . If the first term of a G.P. is ( 2 ) , its common ratio is ( 2 ) and the sum of 2026If the sum of the first 10 terms of the series 1 1 + 1^4 4 + 2 1 + 2^4 4 + 3 1 + 3^4 4 + 4 1 + 4^4 4 + is m n , (m, n) = 1 , then m + n is equal to : 2026Let A₁, A₂, A₃, , A₃₉ be 39 arithmetic means between the numbers 59 and 159 . Then the mean of A₂₅, A₂₈, A₃₁ and A₃₆ is equal to : 2026Let the sum of the first n terms of an A.P. be 3n^2 + 5n . Then the sum of squares of the first 10 terms of the A.P. is: 2026 Full Sequences and Series list All Most Important Selected Qs for JEE Advanced PYQs