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IPMAT Indore 2025

Algebra

>

Progression & Series

Medium

The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the 4th term of the progression is

-48

-24

24

48

✅ Correct Option: 2

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IPMAT Indore 2019

There are numbers

a_1, a_2, a_3, \ldots, a_n

each of them being

+1

-1

. If it is known that

a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0

IPMAT Indore 2019

\alpha, \beta

be the roots of

x^2 - x + p = 0

\gamma, \delta

be the roots of

x^2 - 4x + q = 0

where p and q are integers. If

\alpha, \beta, \gamma, \delta

are in geometric progression then

p + q

IPMAT Indore 2019

(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r

, then the value of

A_2 + A_4 + A_6 + \cdots + A_{12}