Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202420 May 2024Morning ShiftMathematicsSequences and SeriesActual

1 3.7 + 1 7.11 + 1 11.15 + to 50 terms =

Options

  1. A50 203
  2. B50 609
  3. C150 203
  4. D25 609

Correct answer

B. 50 609

Step-by-step solution

1 3.7 + 1 7.11 + 1 11.15 + _n= 1 (4 n-1)(4 n+3) = 1 4 [ 1 4 n-1 - 1 4 n+3 ]T₁= 1 4 [ 1 3 - 1 7 ] T₂= 1 4 [ 1 7 - 1 11 ]T_ n-1 = 1 4 [ 1 4 n-5 - 1 4 n-1 ] S _ n = T ₁+ T ₂+ + T _ n = 1 4 [ 1 3 - 1 4 n+3 ]S_n= n 3(4 n+3) S₅₀= 50 3(200+3) = 50 609

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Every term of a geometric progression is positive , and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is: 2026If k is the arithmetic mean of two given quantities and p, q are the geometric means between the same two quantities, then p^3 + q^3 is: 2026Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 2 2026The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers. 2026Let a₁, a₂, a₃, be a geometric progression of positive integers such that a₁ = 3 and a_ n+2 - 2a_n = a_ n+1 for all positive integers n . What is the value of a₁ + a₂ + a₃ + a₄ + a 2026The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 2026If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are 2026If S _ n =1^3+2^3+ . .+ n ^3 and T _ n =1+2+ . .+ n , then 2025 Full Sequences and Series list All AP EAMCET PYQs