For some natureal number 'n', the sum of the fist 'n' natural numbers is 240 less than the sum of the first `(n+5)` natural numbers. Then n itself is the sum of how many natural numbers starting with 1.

Answer

To solve the problem, we need to find the natural number \( n \) such that the sum of the first \( n \) natural numbers is 240 less than the sum of the first \( n + 5 \) natural numbers. Then, we will determine how many natural numbers starting from 1 sum up to \( n \).

### Step 1: Write the formulas for the sums
The sum of the first \( n \) natural numbers is given by:
\[ S_n = \frac{n(n + 1)}{2} \]
The sum of the first \( n + 5 \) natural numbers is:
\[ S_{n+5} = \frac{(n + 5)(n + 6)}{2} \]

### Step 2: Set up the equation
According to the problem, we have:
\[ S_n + 240 = S_{n + 5} \]
Substituting the formulas we derived:
\[ \frac{n(n + 1)}{2} + 240 = \frac{(n + 5)(n + 6)}{2} \]

### Step 3: Eliminate the fraction
Multiply the entire equation by 2 to eliminate the fraction:
\[ n(n + 1) + 480 = (n + 5)(n + 6) \]

### Step 4: Expand both sides
Expanding both sides gives:
\[ n^2 + n + 480 = n^2 + 11n + 30 \]

### Step 5: Simplify the equation
Subtract \( n^2 \) from both sides:
\[ n + 480 = 11n + 30 \]
Rearranging gives:
\[ 480 - 30 = 11n - n \]
\[ 450 = 10n \]

### Step 6: Solve for \( n \)
Dividing both sides by 10:
\[ n = 45 \]

### Step 7: Find how many natural numbers sum to \( n \)
Now we need to find how many natural numbers starting from 1 sum to \( n \). The sum of the first \( m \) natural numbers is given by:
\[ S_m = \frac{m(m + 1)}{2} \]
We set this equal to \( n \):
\[ \frac{m(m + 1)}{2} = 45 \]
Multiplying by 2:
\[ m(m + 1) = 90 \]

### Step 8: Solve the quadratic equation
Rearranging gives:
\[ m^2 + m - 90 = 0 \]
Using the quadratic formula \( m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):
Here, \( a = 1, b = 1, c = -90 \):
\[ m = \frac{-1 \pm \sqrt{1 + 360}}{2} \]
\[ m = \frac{-1 \pm 19}{2} \]
Calculating the two possible values:
1. \( m = \frac{18}{2} = 9 \)
2. \( m = \frac{-20}{2} = -10 \) (not a natural number)

Thus, \( m = 9 \).

### Final Answer
The number of natural numbers starting from 1 that sum to \( n \) is:
\[ \boxed{9} \]