Find the missing term in the following series.
361, 289, 169, ____, 49
Series Missing Term Identification
The question asks to identify the missing term in the numerical series: 361, 289, 169, ____, 49.
Analyzing the Series Pattern
- Observe the given numbers: 361, 289, 169, 49.
- Recognize that these numbers are perfect squares.
- Calculate the square roots of the known terms:
- $\sqrt{361} = 19$
- $\sqrt{289} = 17$
- $\sqrt{169} = 13$
- $\sqrt{49} = 7$
- Examine the sequence of the square roots: 19, 17, 13, ?, 7.
- Notice that these roots are prime numbers in descending order.
- The sequence of prime numbers is 19, 17, 13, 11, 7.
- The missing prime number in the sequence is 11.
Calculating the Missing Term
The missing term in the original series corresponds to the square of the missing prime root (11).
- Calculate the square of 11: $11^2 = 121$.
Therefore, the missing term in the series is 121.
Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
3, 6, 18, ?, 630, 6930
What should come in place of the question mark ‘?’ in the following number series?
60, 40, 50, ?, 180, 460
A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
