Question:medium

Examine the following numbers and identify the next number:
20, 30, 42, 56, 72, ____

Updated On: Jul 15, 2026
  • 82
  • 90
  • 92
  • 94
Show Solution

The Correct Option is B

Approach Solution - 1

Step 1: Compute the differences between consecutive terms: \(30-20=10\), \(42-30=12\), \(56-42=14\), \(72-56=16\).

Step 2: These differences increase by 2 each time, 10, 12, 14, 16, so the next difference is 18.

Step 3: Add it to the last term: \(72+18=90\).
\[ \boxed{90} \]
Was this answer helpful?
0
Show Solution

Approach Solution -2

The differences between consecutive terms, 10, 12, 14, 16, rise by a constant 2 each time, so the terms fit a quadratic rule \( T(n)=an^2+bn+c \). The constant second difference of 2 gives \( a=1 \). Using \( T(1)=20 \) and \( T(2)=30 \), solving \( 1+b+c=20 \) and \( 4+2b+c=30 \) gives \( b=7 \) and \( c=12 \), so \( T(n)=n^2+7n+12 \). Checking, \( T(3)=9+21+12=42 \), \( T(4)=16+28+12=56 \), \( T(5)=25+35+12=72 \), all correct. The 6th term is \( T(6)=36+42+12=90 \).

  1. Option A (82): plugging \( n=6 \) into the rule gives 90, not 82, and no whole-number \( n \) near the sequence produces 82, so it does not fit.
  2. Option B (90): matches \( T(6)=36+42+12=90 \) exactly, the correct value at position 6.
  3. Option C (92): is 2 more than the rule predicts at \( n=6 \), so it does not satisfy \( T(n)=n^2+7n+12 \).
  4. Option D (94): is 4 more than the rule predicts, further off from the correct value.

Only 90 satisfies the quadratic rule fitted to the first five terms.

Therefore, the correct answer is 90.

Was this answer helpful?
0


Questions Asked in CLAT exam