Series #10

Number Theory Level 1

7, 15, 32, 65, 132, ?, 532

267 265 264 263

Sangeeta Mishra by Sangeeta Mishra , 21, India

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2 solutions

Noel Lo
May 27, 2015

The function from the previous number to the next alternates between these 2 possibilities:

  1. times 2 then plus 1

  2. times 2 then plus 2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Notationally put, the sequence is given by the following recurrence:

∀ n ∈ Z ≥ 2 , a n = { 2 a n − 1 + 1 when n is even 2 a n − 1 + 2 when n is odd \forall~n\in\Bbb{Z_{\geq 2}}~,~a_n=\begin{cases}2a_{n-1}+1\quad\textrm{when }n\textrm{ is even}\\ 2a_{n-1}+2\quad\textrm{when }n\textrm{ is odd}\end{cases}

where the sequence starts with a 1 = 7 a_1=7 .

Clarification: Z ≥ 2 \Bbb{Z_{\geq 2}} refers to the set of all integers greater than or equal to 2 2 .

Prasun Biswas - 6 years ago
Shourya Pandey
Jun 2, 2015

IN the problem the series goes on like at first - x2+1 and then x2+2.....In the third number again its x2+1 and then x2+2 and it continues.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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