Consider the following numerical series: 4, 11, 30, 85, 248, \dots What is the numerical v… — State PSC Exam

Consider the following numerical series:

4, 11, 30, 85, 248, \dots

What is the numerical value of the next term in this series?

Cevap: 735

735

Each term is generated by multiplying the preceding term by 3 and subtracting consecutive odd numbers starting from 1 (

1, 3, 5, 7, 9

). Therefore, the term following 248 is computed as

(248 \times 3) - 9 = 735

Examine the multiplier and subtractor progression between consecutive terms.

Multiplier is constantly 3, while subtractors follow the odd number sequence

1, 3, 5, 7, \dots

Establishing a standard recurrence rule

T_n = 3 \cdot T_{n-1} - (2n - 3)

for

n \ge 2

Calculate the sixth term using the derived rule.

T_6 = (248 \times 3) - 9 = 744 - 9 = 735

The fifth term is 248, and the fifth odd integer to subtract is 9.

Mixed operation numerical series involving constant multiplication and arithmetic progression of subtractors

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