Explanation:

Let's break this down:

- 14 : 21

If we look at this, 14 + 7 = 21. So, the second term is 7 more than the first.

- 34 : ?

If we follow the same pattern, add 7 to 34.

34 + 7 = 41

But hold up—let’s check the next pair for a pattern.

- 47 : 87

47 + 40 = 87

Okay, this jumps by 40. But the gap isn’t the same—first +7, then +40.

Now, let's see if there's a pattern in differences:

21-14 = 7

If we try the options for 34:

Option 1: 61 ? 61-34 = 27

Option 2: 57 ? 57-34 = 23

Option 3: 65 ? 65-34 = 31

Option 4: 53 ? 53-34 = 19

Let's see if these differences make a pattern:

7 (14 to 21)

?? (34 to ?)

40 (47 to 87)

Do you notice a sequence?

The jump from 7 to 40 is +33. So what's halfway?

Maybe they're increasing: 7, then 27 (difference between 61 and 34), then 40.

- 27 is the option matching that kind of progression.

- So, 34 + 27 = 61

So, option 1: 61 is the only answer that comes close to making any sense for a step-wise pattern.

Option 1: 61 is correct.