GMAT Math

please experts,,,,,,,,,,,please help me out through this,,,,,, 3,5,-5.... the first term shown in the sequence is 3 each even numbered term is 2 more than the previous term and odd numbered term, after the first is -1 times the previous term .what is 51st term in the sequence???

Let's look for a pattern:

3, 5, -5...

following their description, the next sequence would continue:

...-3, 3, 5, -5

The 4th term is -3 because it's an even-numbered term and -5 + 2 = -3.
The 5th term is 3 because it's an odd-numbered term and -3 x -1 = 3.

Putting the entire sequence together, we can see a pattern:

3, 5, -5, -3, 3, 5, -5...

There are only 4 unique terms and they repeat on a cycle.

4 divides into 51 evenly 12 times. (12 x 4 = 48), so the cycle will complete on the 48th term.

49th term will then start it again, and be 3.
50th term will be 5.
51st term will be -5.