I need to do list of numbers, which are generated by recursion like

```
a_t = Sum[a_i, {i,0,t-1}]*b

```

I can do it using [`Module`](http://reference.wolfram.com/language/ref/Module.html) and [`Table`](http://reference.wolfram.com/language/ref/Table.html) functions, but is there any possibility to perform it by [`NestList`](http://reference.wolfram.com/language/ref/NestList.html), [`FoldList`](http://reference.wolfram.com/language/ref/FoldList.html) functions.

There is a code with Module and Table, where x0=66,n0=100,shock=0.8 and qstar is a list of mortality rates.

```
detDxt[x0_, n0_, shock_, qstar_, t_] := 
 Module[{DD = Table[Unique[], {t}], i, j},
  DD[[1]] = Round[shock*n0*qstar[[x0]]];
  Table[DD[[i + 1]] = 
    Round[shock*(n0 - Sum[DD[[j]], {j, 1, i}])*qstar[[x0 + i]]], {i, 
    1, t - 2}]; 
  DD[[t]] = 
   Round[(n0 - Sum[DD[[j]], {j, 1, t - 1}])*qstar[[x0 + t - 1]]];
  DD]

```