Replace the question mark (?) in the series given below with the suitable option. 2, 3, 7, 16, 32, ? (a) 57 (b) 37 (c) 48 (d) 55
Answers
ANSWER:
Given:
- Series: 2, 3, 7, 16, 32, ?
To Do:
- Replace question mark with the next term in series
Solution:
Let the missing number (?) be x.
We are given the series,
⇒ 2, 3, 7, 16, 32, x
Now, we will see the difference between every 2 terms, so that we find a pattern.
Hence,
1) 3 - 2 = 1 = 1²
2) 7 - 3 = 4 = 2²
3) 16 - 7 = 9 = 3²
4) 32 - 16 = 16 = 4²
We can see that, the difference of the consecutive terms are perfect square numbers.
That is, series of differences:
⇒ 1², 2², 3², 4²,. . . . .
The next term in this series of differences = 5²
So,
⇒ x - 32 = 5² = 25
⇒ x = 25 + 32
⇒ x = 57
Therefore, the next term in the series is 57(option a).
Answer:
ANSWER:
Given:
Series: 2, 3, 7, 16, 32, ?
To Do:
Replace question mark with the next term in series
Solution:
Let the missing number (?) be x.
We are given the series,
⇒ 2, 3, 7, 16, 32, x
Now, we will see the difference between every 2 terms, so that we find a pattern.
Hence,
1) 3 - 2 = 1 = 1²
2) 7 - 3 = 4 = 2²
3) 16 - 7 = 9 = 3²
4) 32 - 16 = 16 = 4²
We can see that, the difference of the consecutive terms are perfect square numbers.
That is, series of differences:
⇒ 1², 2², 3², 4²,. . . . .
The next term in this series of differences = 5²
So,
⇒ x - 32 = 5² = 25
⇒ x = 25 + 32
⇒ x = 57
Therefore, the next term in the series is 57(option a).