Question:medium

53, 50, 45, 38, 29, ____

Show Hint

When numbers fall quickly but not linearly, try “subtract consecutive odds/evens” or “add consecutive squares/cubes” before more complex rules.
Updated On: Jul 15, 2026
  • 11
  • 17
  • 18
  • 21
Show Solution

The Correct Option is C

Approach Solution - 1

Step 1: Understanding the Concept:
Rather than only looking at the gaps between terms, check if each term fits a simple formula based on its position in the sequence.

Step 2: Key Formula or Approach:
Test whether each term equals \(54 - n^2\), where \(n\) is the position of the term (1 for the first term, 2 for the second, and so on).

Step 3: Detailed Explanation:
For \(n=1\): \(54 - 1 = 53\), matches the first term.
For \(n=2\): \(54 - 4 = 50\), matches the second term.
For \(n=3\): \(54 - 9 = 45\), matches the third term.
For \(n=4\): \(54 - 16 = 38\), matches the fourth term.
For \(n=5\): \(54 - 25 = 29\), matches the fifth term.
Since the formula holds for every given term, the sixth term (\(n=6\)) should equal \(54 - 36 = 18\).

Step 4: Final Answer:
The missing number is 18.
\[ \boxed{18} \]
Was this answer helpful?
0
Show Solution

Approach Solution -2

Step 1: Understanding the Concept:
The gaps between consecutive terms, 3, 5, 7, 9 (all subtracted), are consecutive odd numbers, and consecutive odd numbers follow the general formula \(2k+1\) for the \(k\)-th gap, starting at \(k=1\).

Step 2: Key Formula or Approach:
Write the gap between term \(k\) and term \(k+1\) as \(2k+1\), and use \(k=5\) to find the gap between the fifth and sixth terms directly, without listing every earlier gap first.

Step 3: Detailed Explanation:
Checking the formula against the known gaps: for \(k=1\), \(2(1)+1=3\), matching the drop from 53 to 50. For \(k=2\), \(2(2)+1=5\), matching the drop from 50 to 45. For \(k=3\), \(2(3)+1=7\), matching the drop from 45 to 38. For \(k=4\), \(2(4)+1=9\), matching the drop from 38 to 29.
For the gap between the fifth and sixth terms, \(k=5\): \(2(5)+1=11\).
So the sixth term is \(29 - 11 = 18\).

Step 4: Final Answer:
The missing number is 18.
\[ \boxed{18} \]
Was this answer helpful?
0

Top Questions on Series

Questions Asked in CLAT exam

Read the passage and answer the question.

Passage (extract): The work which Gandhiji had taken up was not only regarding the achievement of political freedom but also the establishment of a new social order based on truth and non-violence, unity and peace, equality and universal brotherhood and maximum freedom for all. A new order cannot be established without radically changing the mind and attitude of men towards property and, at some stage or the other, the 'haves' have to yield place to the 'have-nots'. We have seen, in our time, attempts to achieve a kind of egalitarian society and the picture of it after it was achieved. But this was done, by and large, through the use of physical force. It may even be that, like a gas kept confined within containers under great pressure, or water held back by a big dam, once the barrier breaks, the reaction will one day sweep back with a violence equal in extent and intensity to what was used to establish and maintain the outward egalitarian form. This enforced egalitarianism contains, in its bosom, the seed of its own destruction. If egalitarianism is to endure, it has to be based not on the possession of the maximum material goods by a few or by all but on voluntary, enlightened renunciation of those goods which cannot be shared by others or can be enjoyed only at the expense of others.

According to the passage, egalitarianism will not survive if
View Solution
Read the passage and answer the question.

Passage (extract): The work which Gandhiji had taken up was not only regarding the achievement of political freedom but also the establishment of a new social order based on truth and non-violence, unity and peace, equality and universal brotherhood and maximum freedom for all. This unfinished part of his experiment was perhaps even more difficult to achieve than the achievement of political freedom. In the political struggle, the fight was against a foreign power and all one could do was either join it or wish it success and give it his/her moral support. In establishing a social order on this pattern, there was a strong possibility of a conflict arising between diverse groups and classes of our own people.

According to the passage, which was the unfinished part of Gandhi's experiment?
View Solution
Read the passage and answer the question.

Passage (extract): In the political struggle, the fight was against a foreign power and all one could do was either join it or wish it success and give it his/her moral support. Experience shows that man values his possessions even more than his life because in the former he sees the means for perpetuation and survival of his descendants even after his body is reduced to ashes. We have seen, in our time, attempts to achieve a kind of egalitarian society and the picture of it after it was achieved. But this was done, by and large, through the use of physical force. This enforced egalitarianism contains, in its bosom, the seed of its own destruction. The root cause of class conflict is possessiveness or the acquisitive instinct.

Which of the following statements is 'not true' in the context of the passage?
View Solution