Question:
Find the missing term in the series:
\[ 8,\ 18,\ 38,\ 78,\ 158,\ 318,\ \underline{\hspace{1cm}} \]
Find the missing term in the series:
\[ 8,\ 18,\ 38,\ 78,\ 158,\ 318,\ \underline{\hspace{1cm}} \]
Show Hint
If the numbers grow rapidly, first check multiplication-based patterns such as \(2n+c\), \(3n+c\), or powers.
Updated On: Jun 13, 2026
- 618
- 628
- 638
- 648
Show Solution
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The Correct Option is C
Solution and Explanation
Concept:
Many number series are formed by multiplying a term by a fixed number and then adding or subtracting a constant.
Step 1: Observe the relationship between consecutive terms. \[ 8\times2+2=18 \] \[ 18\times2+2=38 \] \[ 38\times2+2=78 \] \[ 78\times2+2=158 \] \[ 158\times2+2=318 \] Thus the rule is \[ a_{n+1}=2a_n+2. \]
Step 2: Apply the rule to obtain the next term. \[ 318\times2+2 = 636+2 = 638. \] Therefore the required term is \[ \boxed{638}. \]
Step 1: Observe the relationship between consecutive terms. \[ 8\times2+2=18 \] \[ 18\times2+2=38 \] \[ 38\times2+2=78 \] \[ 78\times2+2=158 \] \[ 158\times2+2=318 \] Thus the rule is \[ a_{n+1}=2a_n+2. \]
Step 2: Apply the rule to obtain the next term. \[ 318\times2+2 = 636+2 = 638. \] Therefore the required term is \[ \boxed{638}. \]
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