Run sequence of tasks, one after the other

I have a sequence of tasks, where each one depends on the output of the previous one. I'd like to represent this as a single Task object, whose result is the output of the end of the sequence. (If the tasks didn't depend on one another then I could do it in parallel and I would use TaskFactory.ContinueWhenAll.)

I'd like to be able to implement this method:

static Task<TState> AggregateAsync<T, TState>(
    IEnumerable<T> items,
    TState initial,
    Func<TState, T, Task<TState>> makeTask);

How can I efficiently run the tasks one after another in sequence? I'm using C# 4.0 so I can't use async/await to do it for me.

Edit: I could write AggregateAsync like this:

static Task<TState> AggregateAsync<T, TState>(IEnumerable<T> items, TState initial, Func<TState, T, Task<TState>> makeTask)
{
    var initialTask = Task.Factory.StartNew(() => initial);
    return items.Aggregate(
        initialTask,
        (prevTask, item) =>
            {
                prevTask.Wait(); // synchronous blocking here?
                return makeTask(prevTask.Result, item);
            });
}

But surely I'll get a batch of tasks, each of which blocks synchronously waiting for the one before it?