Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2015MathematicsSequences and Series

The sum to n terms of the series 3 1^2 + 5 1^2+2^2 + 7 1^2+2^2+3^2 + , is

Options

  1. A6 n n+1
  2. B9 n n+1
  3. C12 n n+1
  4. D3 n n+1

Correct answer

A. 6 n n+1

Step-by-step solution

Let T_r be the r th term of the given series. Then, T_r= 2 r+1 1^2+2^2+ +r^2 = 2 r+1 r(r+1)(2 r+1) 6 = 6 r(r+1) T_r=6 ( 1 r - 1 r+1 ) So, the required sum is given by _ r=1 ^n T_r=6 _ r=1 ^n ( 1 r - 1 r+1 ) aligned & =6 [ 1 1 - 1 2 + 1 2 - 1 3 + + 1 n - 1 n+1 ] & =6 [1- 1 n+1 ]= 6 n n+1 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 Manipal MET PYQs