How to get weighted average where latest value is weighted twice as all previous?

Question

I've used this before, but just can't remember it, and can't find it anywhere.

It's a running average where the newest value has twice the weight of all the previous values (combined), so that as time passes the oldest values have less and less effect. And I don't have enough memory to store the older values.

TO GET AVERAGE:

int sum=0;
int n = 0;
float aver = 0;
for(;;){
  float new_value = some_function();
  sum += new_value;
  ++n;
  aver = sum / n;  
}

But how to I get an average where the new_value is weighted to be twice the weighting of the previous average?

float aver = 0;
for(;;){
  float new_value = some_function();
  aver = aver * ??? + new_value * ???;

}

Answer 1

a running average where the newest value has twice the weight of all the previous values, ...

how to I get an average where the new_value is weighted to be twice the weighting of the previous average?

Compute the special average on the sum and the latest.

int sum = 0;
int n = 0;
float average_special = 0.0;
for(;;) {
  float new_value = some_function();
  sum += new_value;
  ++n;
  average_special = (sum + new_value) / (n+1);  
}