99 Percentile Qs Bank for JEE MainMathematicsSequences and Series

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

Options

A22.5
B24.5
C28.5
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

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: 2026 The sum 1 + 1 2 (1^2 + 2^2) + 1 3 (1^2 + 2^2 + 3^2) + upto 10 terms is equal to : 2026 The value of 1^3 - 2^3 + 3^3 - + 15^3 is: 2026 The 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 2026 For 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 2026 If 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 : 2026 Let 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 : 2026 Let 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 99 Percentile Qs Bank for JEE Main PYQs