Analyze the pattern in the numerical sequence given below: 4, \quad 9, \quad 20, \quad 43,… — State PSC Exam

Analyze the pattern in the numerical sequence given below:

4, \quad 9, \quad 20, \quad 43, \quad 90, \quad ?

What is the value of the missing term that completes the sequence?

Answer: 185

185

Each consecutive term is calculated by doubling the previous term and adding an increasing integer (

+1, +2, +3, +4, +5

). Following this rule,

90 \times 2 + 5 = 185

Examine differences or operations between adjacent terms

9 - 4 = 5

20 - 9 = 11

43 - 20 = 23

90 - 43 = 47

Identify the primary numerical increment pattern

Analyze the rule for term progression

The operations follow

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

for

n \ge 2

Confirm consistency across all given terms

Compute the sixth term (

T_6

)

T_6 = 90 \times 2 + 5 = 185

Apply the addition increment

+5

following

+4

Number and Alphabet Series

Question