Number Series, Coding, Odd Man OutPYQ June 22Question 2028 of 217
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Find out the next term −6,13,28,59,?\displaystyle -6, 13, 28, 59, ?

Options

A122
B114
C113
D112
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 122

All Options:

  • A122
  • B114
  • C113
  • D112

Detailed Solution & Explanation

We are given the series: −6,13,28,59,?\displaystyle -6, 13, 28, 59, ?
**Discrepancy Note:**
The negative sign in front of the first term 6\displaystyle 6 is a typographical error in the question paper; the first term should be 6\displaystyle 6 instead of −6\displaystyle -6. Using 6\displaystyle 6, we get the series 6,13,28,59,?\displaystyle 6, 13, 28, 59, ?.
Let's analyze the recurrence relation:
xn=2xn−1+(n−1)for n≥2x_n = 2 x_{n-1} + (n-1) \quad \text{for } n \ge 2
Let's verify:
- x1=6\displaystyle x_1 = 6
- x2=2(6)+1=13\displaystyle x_2 = 2(6) + 1 = 13
- x3=2(13)+2=28\displaystyle x_3 = 2(13) + 2 = 28
- x4=2(28)+3=59\displaystyle x_4 = 2(28) + 3 = 59
Following this pattern, the next term is:
x5=2(59)+4=118+4=122x_5 = 2(59) + 4 = 118 + 4 = 122
Hence, **Option A** is the correct answer.

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