Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024MathematicsSequences and Series

The value of 1 1 4 + 1 4 7 + 1 7 10 + + 1 (3 n-2)(3 n+1) is

Options

  1. An 3 n+1
  2. Bn 3 n+2
  3. C-n 3 n+1
  4. D-n 3 n+2

Correct answer

A. n 3 n+1

Step-by-step solution

aligned & 1 1 4 + 1 4 7 + 1 7 10 + + 1 (3 n-2)(3 n+1) & aligned & 1 3 [ 4-1 1 4 + 7-4 4 7 + 10-7 7 10 + + (3 n+1)-(3 n-2) (3 n-2)(3 n+1) ] = & 1 3 [ 4 1 4 - 1 1 4 + 7 4 7 - 4 4 7 + 10 7 10 - 7 7 10 . & .+ + 1 3 n-2 - 1 3 n+1 ] = & 1 3 [ 1 1 - 1 4 + 1 4 - 1 7 + 1 7 - 1 10 + + 1 3 n-2 - 1 3 n+1 ] = & 1 3 [1- 1 3 n+1 ]= 3 n 3(3 n+1) = n 3 n+1 aligned aligned

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 COMEDK PYQs