JEE Main 2023 (Online) 1st February Morning Shift | Sequences and Series Question 119 | Mathematics

Let $a_1, a_2, a_3, \ldots$ be an A.P. If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :

$\frac{381}{4}$

$\frac{33}{4}$

JEE Main 2023 (Online) 31st January Morning Shift

MCQ (Single Correct Answer)

-1

If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

$$\frac{9}{2}$$

JEE Main 2023 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

-1

Let $a, b, c>1, a^3, b^3$ and $c^3$ be in A.P., and $\log _a b, \log _c a$ and $\log _b c$ be in G.P. If the sum of first 20 terms of an A.P., whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to :

343

216

$\frac{343}{8}$

$\frac{125}{8}$

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