Answer:

A.

1.

A quick puzzle for you — look at the first few square numbers:

1, 4, 9, 16, 25, 36, 49…

And now find the difference between consecutive squares:

1 to 4 = 3

4 to 9 = 5

9 to 16 = 7

16 to 25 = 9

25 to 36 = 11

…

2.

As can be observed, every term in the given sequence: 2, 4, 6, 8, ..., is an even positive integer, and is, therefore, a multiple of 2:

1st term: 2 = 2(1)

2nd term: 4 = 2(2)

3rd term: 6 = 2(3)

4th term: 8 = 2(4)

Additional terms:

5th term: 10 = 2(5)

6th term: 12 = 2(6)

7th term: 14 = 2(7)

8th term: 16 = 2(8)

Therefore, using this same pattern, we see that the nth term of the given sequence is: 2n, where n is a positive integer that indicates the desired term of the sequence. For example, the 500th term of the sequence is: 2n = 2(500) = 1,000.

3.

The next number of the sequence 3, 5, 9, 17, 33 …. is :

[A]49

[B]60

[C]65

[D]50

65

3\xrightarrow{+2}5\xrightarrow{+4=2^{2}}9\xrightarrow{+8 = 2^{3}}17\xrightarrow{+16= 2^{4}}33\xrightarrow{+32 = 2^{5}}\underline{65}

∴ The next term in the sequence will be 65.

Hence option [C] is the right answer.