Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series
If a₁, a₂, a₃, , , are in arithmetic progression, then S=a₁^2-a₂^2+a₃^2-a₄^2+ -a_ 2 k ^2 is equal to:
Options
- Ak 2 k-1 (a₁^2-a_ 2 k ^2 )
- B2 k k-1 (a_ 2 k ^2-a₁^2 )
- Ck k+1 (a₁^2-a_ 2 k ^2 )
- Dnone of these
Correct answer
A. k 2 k-1 (a₁^2-a_ 2 k ^2 )
Step-by-step solution
S=-d (a₁+a₂+ +a_ 2 k ) , where d is common difference S=-d 2 k 2 (a₁+a_ 2 k )=-k d (a₁+a_ 2 k )........(1) Now, aligned & a₂-a₁=d & a₃-a₂=d aligned a_ 2 k -a_ 2 k-1 =d a_ 2 k -a₁=(2 k-1) d Add a_ 2 k -a_ 2 k-1 =d a_ 2 k -a₁=(2 k-1) d ........(2) From eqn. (1) and eqn. (2) S= k 2 k-1 (a₁^2-a_ 2 k ^2 )