JEE Main 2025 (Online) 2nd April Evening Shift | Sequences and Series Question 45 | Mathematics

The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :

JEE Main 2025 (Online) 2nd April Morning Shift

MCQ (Single Correct Answer)

-1

Let $a_1, a_2, a_3, \ldots$ be in an A.P. such that $\sum_\limits{k=1}^{12} a_{2 k-1}=-\frac{72}{5} a_1, a_1 \neq 0$. If $\sum_\limits{k=1}^n a_k=0$, then $n$ is :

JEE Main 2025 (Online) 29th January Morning Shift

MCQ (Single Correct Answer)

-1

Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11^th term is :

108

122

JEE Main 2025 (Online) 28th January Evening Shift

MCQ (Single Correct Answer)

-1

For positive integers $n$, if $4 a_n=\left(n^2+5 n+6\right)$ and $S_n=\sum\limits_{k=1}^n\left(\frac{1}{a_k}\right)$, then the value of $507 S_{2025}$ is :

540

675

1350

135

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