3 7 14 27 52

Subtract the integers starting with 0, which has nth term n-1

0 1  2  3  4

That gives:

3 6 12 24 48     

That's a geometric series with nth term 3∙2n-1

So the general term is

3∙2n-1 + n - 1

Checking by substituting n=1...5

3∙21-1 + 1 - 1 = 3∙20+0 = 3∙1 = 3
3∙22-1 + 2 - 1 = 3∙21+1 = 3∙2+1 = 6+1 = 7
3∙23-1 + 3 - 1 = 3∙22+2 = 3∙4+2 = 12+2 = 14
3∙24-1 + 4 - 1 = 3∙23+3 = 3∙8+3 = 24+3 = 27
3∙25-1 + 5 - 1 = 3∙23+1 = 3∙16+4 = 48+5 = 52

It checks.

Edwin