Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2014MathematicsSequences and SeriesActual

The sum of the first 20 terms common between the series 3+7+11+15+ and 1+6+11+16+ . . is

Options

  1. A4000
  2. B4020
  3. C4200
  4. D4220

Correct answer

B. 4020

Step-by-step solution

Given n =20 ; S ₂₀= ? Series (1) 3,7, 11 , 15,19,23,27, 31 , 35 , 39,43,47 , 51 , 55,59 Series (2) 1,6, 11 , 16,21,26, 31 , 36,41 , 46, 51 , 56 , 61,66,71 . The common terms between both the series are 11,31,51,71 Above series forms an Arithmetic progression (A.P). Therefore, first term (a) =11 and common difference ( d )=20 Now, S _ n = n 2 [2 a+(n-1) d] aligned & S ₂₀= 20 2 [2 11+(20-1) 20] & S ₂₀=10[22+19 20] & S ₂₀=10 402=4020 & S ₂₀=4020 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 JEE Main PYQs