IPMAT Indore 2022 (SA) PYQs

There are numbers $a_1, a_2, a_3, \ldots, a_n$ each of them being $+1$ or $-1$. If it is known that $a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0$ then

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of $n$ for which the sum of its first $n$ terms is closest to 100, is

The number of terms common to both the arithmetic progressions $2, 5, 8, 11, ..., 179$ and $3, 5, 7, 9, ..., 101$ is