Question:
Find the missing term in the series:
\[ 2,\ 6,\ 20,\ 42,\ 110,\ 156,\ \underline{\hspace{1cm}} \]
Find the missing term in the series:
\[ 2,\ 6,\ 20,\ 42,\ 110,\ 156,\ \underline{\hspace{1cm}} \]
Show Hint
When differences appear irregular, try factorizing the terms. Hidden multiplication patterns often emerge immediately.
Updated On: Jun 13, 2026
- 262
- 272
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- 282
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The Correct Option is B
Solution and Explanation
Concept:
The terms are generated using products of consecutive prime numbers.
Step 1: Express each term in factorized form. \[ 2=1\times2 \] \[ 6=2\times3 \] \[ 20=4\times5 \] \[ 42=6\times7 \] \[ 110=10\times11 \] \[ 156=12\times13 \] Observe that each term is obtained by multiplying two consecutive numbers, where the second factor is the next prime.
Step 2: Continue the pattern. After \[ 12\times13, \] the next suitable pair is \[ 16\times17. \] Therefore \[ 16\times17 = 272. \] Hence the missing term is \[ \boxed{272}. \]
Step 1: Express each term in factorized form. \[ 2=1\times2 \] \[ 6=2\times3 \] \[ 20=4\times5 \] \[ 42=6\times7 \] \[ 110=10\times11 \] \[ 156=12\times13 \] Observe that each term is obtained by multiplying two consecutive numbers, where the second factor is the next prime.
Step 2: Continue the pattern. After \[ 12\times13, \] the next suitable pair is \[ 16\times17. \] Therefore \[ 16\times17 = 272. \] Hence the missing term is \[ \boxed{272}. \]
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