A Simple Pattern Pt.2

The first term of the sequence must be supplied. Let it be $x$ . Then the sequence is $(x+1),2(x+1),4(x+1),8(x+1),...2^i(x+1),....$ .

Of the given options, only $16384=2^{14}$ is a multiple of a power of $2$ , no others are. So that is the correct option.

We first look for a pattern. We start off by testing the first few terms. 1,2,4,8,16,... So there obviously is a pattern. From here, we have a few solutions.

Solution 1: Brute force

List until you get the 15th term: 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384

So the answer is 16384

Solution 2: Powers of 2

We can see that the nth term is 2^(n-1), so the 15th term is 2^14=16384

Why it's true:

Lets suppose n=1

Then the first few terms are few terms are n,n+1,2n+2 (4n), 4n+4 (8n), 8n+8(16n),...

So the terms are (2^0)n, (2^1)n,...