Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2004MathematicsSequences and Series

_ k=1 ^5 1^3+2^3+ +k^3 1+3+5+ +(2 k-1) is equal to

Options

  1. A22.5
  2. B24.5
  3. C28.5
  4. D32.5

Correct answer

A. 22.5

Step-by-step solution

aligned & _ k=1 ^5 1^3+2^3+ +k^3 1+3+5+ .+(2 k-1) & = _ k=1 ^5 ( k(k+1) 2 )^2 k^2 & [ array l n^3= ( n(n+1) 2 )^2 and 1+3+5 +(2 K-1)=K^2 array ] & = _ k=1 ^5 (k+1)^2 4 = 2^2+3^2+4^2+5^2+6^2 4 & = 4+9+16+25+36 4 = 90 4 =22.5 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 AP EAMCET PYQs