JEE Main & Advanced
Mathematics
Sequence & Series
Question Bank
Numerical Value Type Questions - Progressions
question_answer
Let \[{{a}_{n}}\] be the nth term of an A.P. If \[\sum\limits_{r=1}^{100}{{{a}_{2r}}}=\alpha \] and \[\sum\limits_{r=1}^{100}{{{a}_{2r-1}}}=\beta \], and the common difference of A.P. is \[\frac{\alpha -\beta }{\lambda }\] then find \[\lambda \].