1
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

Let $$a_{1}=8, a_{2}, a_{3}, \ldots, a_{n}$$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is ___________.

2
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Out of Syllabus
The sum $1^{2}-2 \cdot 3^{2}+3 \cdot 5^{2}-4 \cdot 7^{2}+5 \cdot 9^{2}-\ldots+15 \cdot 29^{2}$ is _________.
3
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

Let $$a_{1}, a_{2}, \ldots, a_{n}$$ be in A.P. If $$a_{5}=2 a_{7}$$ and $$a_{11}=18$$, then

$$12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$$ is equal to ____________.

4
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
Out of Syllabus
The $8^{\text {th }}$ common term of the series

\begin{aligned} & S_1=3+7+11+15+19+\ldots . . \\\\ & S_2=1+6+11+16+21+\ldots . . \end{aligned}

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