Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2012MathematicsSequences and SeriesActual

Let a₁, a₂, a₃, . . be in harmonic progression with a₁=5 and a₂₀=25 . The least positive integer n for which a_ n < 0 is

Options

  1. A22
  2. B23
  3. C24
  4. D25

Correct answer

D. 25

Step-by-step solution

a₁, a₂, a₃, are in H.P. array l 1 a₁ , 1 a₂ , 1 a₃ are in A.P. 1 a₁ = 1 5 and 1 a₂₀ = 1 25 1 a₁ +19 d= 1 a₂₀ 1 5 +19 d= 1 25 d= -4 475 Now 1 a_ n = 1 5 +(n-1) ( -4 475 ) Clearly a_ n 99 4 =24 3 4 n 25 Least value of n is 25 . array

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 JEE Advanced PYQs