Can you solve this tricky series? What number comes next in the series: 5, 11, 23, 47, 95, …?

 Can you solve this tricky series? What number comes next in the series: 5, 11, 23, 47, 95, …?👇🏿👇🏿👇🏿👇🏿👇🏿👇🏿👇🏿👇🏿👇 🏿

To determine the next number in the series $5,11,23,47,95,\dots$, let's first observe the pattern of how each term is generated from the previous one.

We start by examining the differences between consecutive terms:

$$\begin{array}{rl}{\displaystyle \mathrm{<b>11</b>}<b>-</b>\mathrm{<b>5</b>}}& {\displaystyle <b>=</b>\mathrm{<b>6</b>}<b>,</b>}\\ {\displaystyle \mathrm{<b>23</b>}<b>-</b>\mathrm{<b>11</b>}}& {\displaystyle <b>=</b>\mathrm{<b>12</b>}<b>,</b>}\\ {\displaystyle \mathrm{<b>47</b>}<b>-</b>\mathrm{<b>23</b>}}& {\displaystyle <b>=</b>\mathrm{<b>24</b>}<b>,</b>}\\ {\displaystyle \mathrm{<b>95</b>}<b>-</b>\mathrm{<b>47</b>}}& {\displaystyle <b>=</b>\mathrm{<b>48.</b>}}\end{array}$$

Now, let's list these differences:

$$6,12,24,48.$$

Next, observe the pattern in the differences:

$$\begin{array}{rl}{\displaystyle \mathrm{<b>12</b>}<b>-</b>\mathrm{<b>6</b>}}& {\displaystyle <b>=</b>\mathrm{<b>6</b>}<b>,</b>}\\ {\displaystyle \mathrm{<b>24</b>}<b>-</b>\mathrm{<b>12</b>}}& {\displaystyle <b>=</b>\mathrm{<b>12</b>}<b>,</b>}\\ {\displaystyle \mathrm{<b>48</b>}<b>-</b>\mathrm{<b>24</b>}}& {\displaystyle <b>=</b>\mathrm{<b>24.</b>}}\end{array}$$

It appears that the differences between consecutive terms in the differences are $6,12,24$, and the difference between each term and the next is doubling. This suggests the next difference should be $48\times 2=96$.

Now, to find the next term in the original series, we add this new difference to the last term:

$$\mathrm{<b>95</b>}<b>+</b>\mathrm{<b>96</b>}<b>=</b>\mathrm{<b>191.</b>}$$

Thus, the next number in the series is: 191 (ANS)