Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2015MathematicsSequences and SeriesActual

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178 . If the first term of this A.P. is 10 , then the median of the A.P. is :

Options

  1. A26 . 5
  2. B29 . 5
  3. C28
  4. D31

Correct answer

B. 29 . 5

Step-by-step solution

Let the A.P. be a ,   a + d , a + 2 d ⋯ ⋯ , l - 3 d ,   l - 2 d ,   l - d , l Where a is the first term and l is the last term, Sum of 1 s t , 3 terms is, 39 . 30 + 3 d = 39 as a = 10 (Given) d = 9 3 = 3 Sum of last 4 terms is 178 . 4 l - 6 d = 178 l = 49 10 ,   13 ,   16 ,   19 . . . . . . . 46 ,   49 Let number of terms are, n then n t h term is 10   +   ( n   -   1 )   3   =   49 ⇒ n   =   14 So the median of the se

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 Main PYQs