JEE Main 2025 (Online) 3rd April Morning Shift | Sequences and Series Question 10 | Mathematics

Let $a_1, a_2, a_3, \ldots$. be a G.P. of increasing positive numbers. If $a_3 a_5=729$ and $a_2+a_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to

128

129

131

130

JEE Main 2025 (Online) 3rd April Morning Shift

MCQ (Single Correct Answer)

-1

The sum $1+3+11+25+45+71+\ldots$ upto 20 terms, is equal to

7240

8124

7130

6982

JEE Main 2025 (Online) 2nd April Evening Shift

MCQ (Single Correct Answer)

-1

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 :