x 17 3x ndash y2 2 and 3x y2 30 are four consecutive terms of an increasing arithmetic sequence The ...........

Quantitative Aptitude ( CCS) Arithmetic progression

x, 17, 3x – y² - 2 and 3x + y² - 30 are four consecutive terms of an increasing arithmetic sequence. The sum of the 4 numbers is divisible by:

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Explanation:

Of all the 4 terms in AP, the 2^nd term is 17, which is an odd number.
The common difference has to be either even or odd.
Possibility 1: If the common difference is odd, 1st term will be even, 3rd term will be even and the 4th term will be odd.
i.e., two of the terms of the sequence are odd & two are even.
Sum of two odd numbers and two even numbers is even.
Possibility 2: If common difference is even, all 4 terms will be odd.
Sum of 4 odd numbers is even.
So, irrespective of whether common difference is odd or even, the sum of four terms is even.
Hence, the sum will be divisible by 2