Determine the value of the missing term that logically continues the given numerical seque… — State PSC Exam

Determine the value of the missing term that logically continues the given numerical sequence:

6, 13, 28, 59, 122, ?

Cevap: 249

The missing term in the sequence is 249.

The sequence follows the pattern

T_n = T_{n-1} \times 2 + (n-1)

for

n \ge 2

. Thus, the 6th term is

122 \times 2 + 5 = 249

Examine the transition between consecutive numbers in the series

From 6 to 13:

6 \times 2 + 1 = 13

From 13 to 28:

13 \times 2 + 2 = 28

Establishing the basic recursive function pattern

Verify the pattern across remaining terms

From 28 to 59:

28 \times 2 + 3 = 59

From 59 to 122:

59 \times 2 + 4 = 122

Confirming that the multiplier is constant (2) while the added constant increments by 1 at each step

Apply the rule to find the missing term

122 \times 2 + 5 = 244 + 5 = 249

Extending the pattern by adding 5 after doubling the previous term

Recursive series with constant multiplier and arithmetic additive offset

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