Find the next term: 3, 7, 15, 31, 63, ?

127. Each term is double the previous term plus 1: 63 2 + 1 = 127. (Equivalently the terms are 2^n - 1.)

Find the missing term: 5, 11, 23, 47, ?, 191

95. Each term is double the previous term plus 1: 47 2 + 1 = 95, and 95 2 + 1 = 191 confirms it.

Which number does not belong in the series 4, 9, 16, 25, 35, 49?

35. The series lists perfect squares 2^2, 3^2, 4^2, 5^2, \, 7^2. The term after 25 should be 6^2 = 36, so 35 is the odd one out.

Find the next term: 2, 6, 12, 20, 30, ?

42. The differences are 4, 6, 8, 10, so the next difference is 12: 30 + 12 = 42. (Each term equals n(n+1).)

Find the wrong term: 1, 8, 27, 64, 125, 218, 343

218. The series is the perfect cubes 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3. The sixth term should be 6^3 = 216, not 218.

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Quantitative Aptitude · Numbers & Simplification

Odd One Out & Number Series — Questions & Answers

Number series questions give a sequence built on a hidden rule — a constant difference, a ratio, squares, cubes, or an alternating pattern. Your job is to spot the rule and then find the missing term or the term that does not fit.

5 solved questions
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Key formulas included

Key formulas

Arithmetic progression: each term differs by a fixed $d$ ; $n$ -th term $= a + (n-1)d$
Geometric progression: each term is a fixed multiple $r$ of the previous; $n$ -th term $= a\,r^{\,n-1}$
Check for squares ( $1,4,9,16,\dots$ ), cubes ( $1,8,27,64,\dots$ ) and prime sequences
For alternating series, separate the odd-position and even-position terms and test each

5 solved Odd One Out & Number Series questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
Find the next term: 3, 7, 15, 31, 63, ?
4 steps · reveal one at a time
1. Step 1: Find the Pattern
  We need to identify the mathematical rule that generates each term from the previous one in the sequence $3, 7, 15, 31, 63, ?$ . Let's look at the differences or relationships.
2. Step 2: Identify the Rule
  Let's examine the relationship between consecutive terms: \n $3 \times 2 + 1 = 7$ \n $7 \times 2 + 1 = 15$ \n $15 \times 2 + 1 = 31$ \n $31 \times 2 + 1 = 63$ . \nThe pattern is to double the previous term and add 1.
3. Step 3: Calculate Next Term
  Now, apply this rule to the last given term, $63$ , to find the next number in the sequence. \nNext term $= 63 \times 2 + 1$ . \n $63 \times 2 = 126$ . \n $126 + 1 = 127$ .
4. Step 4: The answer
  So the answer is (B) 127, because following the pattern of doubling the previous term and adding 1 gives $63 \times 2 + 1 = 127$ .
02
Find the missing term: 5, 11, 23, 47, ?, 191
5 steps · reveal one at a time
1. Step 1: Look for a pattern
  Let's examine the relationship between consecutive terms in the sequence: $5, 11, 23, 47, ?, 191$ . We need to find a rule that connects them.
2. Step 2: Identify the rule
  Let's try multiplication and addition. From 5 to 11, we see $5 \times 2 + 1 = 11$ . From 11 to 23, it's $11 \times 2 + 1 = 23$ . From 23 to 47, it's $23 \times 2 + 1 = 47$ . The rule is: double the previous term and add 1.
3. Step 3: Calculate missing term
  Now, apply this rule to the last known term, 47, to find the missing term. The missing term is $47 \times 2 + 1 = 94 + 1 = 95$ .
4. Step 4: Verify the sequence
  To be sure, let's check if our rule holds for the next term using 95. We calculate $95 \times 2 + 1 = 190 + 1 = 191$ . This matches the last term in the given sequence, confirming our rule.
5. Step 5: The answer
  So the answer is (C) 95, because applying the rule "double the previous term and add 1" to 47 gives 95, and this rule is consistent throughout the sequence.
03
Which number does not belong in the series 4, 9, 16, 25, 35, 49?
4 steps · reveal one at a time
1. Step 1: Identify the pattern
  Let's look at the given numbers: 4, 9, 16, 25, 35, 49. Many of these are perfect squares. We can write them as $2^2=4$ , $3^2=9$ , $4^2=16$ , $5^2=25$ , and $7^2=49$ .
2. Step 2: Find the missing term
  The pattern seems to be consecutive integers squared: $2^2, 3^2, 4^2, 5^2, \dots, 7^2$ . Following this sequence, the number after $5^2=25$ should be $6^2$ .
3. Step 3: Calculate expected value
  If the pattern holds, the term after 25 should be $6^2 = 36$ . However, the series lists 35 in that position. All other numbers fit the perfect square pattern.
4. Step 4: The answer
  So the answer is (A) 35. This number does not fit the pattern of consecutive perfect squares, as it should be $6^2=36$ instead of 35.
04
Find the next term: 2, 6, 12, 20, 30, ?
4 steps · reveal one at a time
1. Step 1: Look for a pattern
  Let's find the difference between consecutive terms in the sequence: $2, 6, 12, 20, 30$ . The first difference is $6 - 2 = 4$ . The next is $12 - 6 = 6$ . Then $20 - 12 = 8$ , and $30 - 20 = 10$ .
2. Step 2: Identify the rule
  The differences we found are $4, 6, 8, 10$ . This is a sequence of even numbers increasing by 2 each time. So, the next difference in this sequence should be $10 + 2 = 12$ .
3. Step 3: Calculate the next term
  To find the next term in the original sequence, we add this next difference to the last given term. The last term is $30$ , and the next difference is $12$ . So, the next term is $30 + 12 = 42$ .
4. Step 4: The answer
  So the answer is (B) 42, because adding the next difference of 12 to 30 gives us 42, following the established pattern.
05
Find the wrong term: 1, 8, 27, 64, 125, 218, 343
4 steps · reveal one at a time
1. Step 1: Examine the series
  Let's look at the given series: $1, 8, 27, 64, 125, 218, 343$ . Try to find a relationship between consecutive terms or recognize a common mathematical sequence.
2. Step 2: Identify the pattern
  Notice that many of these numbers are perfect cubes. For example, $1 = 1^3$ , $8 = 2^3$ , $27 = 3^3$ , $64 = 4^3$ , and $125 = 5^3$ . The last term, $343$ , is also $7^3$ .
3. Step 3: Find the outlier
  Following the pattern, the sixth term should be $6^3$ . Let's calculate $6^3 = 6 \times 6 \times 6 = 36 \times 6 = 216$ . However, the given sixth term is $218$ . This is the wrong term.
4. Step 4: The answer
  So the answer is (D) 218. The series should consist of perfect cubes, and $218$ does not fit the pattern as $6^3$ is $216$ , not $218$ .

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