To find the sum of the multiples of 4 from 16 to 100, we start by identifying the first and last multiples of 4 within that range.
The first multiple of 4 in this range is 16, and the last multiple of 4 before reaching 100 is 100 itself, as 100 is also a multiple of 4.
Now, we can enumerate the multiples of 4 from 16 to 100:
- 16
- 20
- 24
- 28
- 32
- 36
- 40
- 44
- 48
- 52
- 56
- 60
- 64
- 68
- 72
- 76
- 80
- 84
- 88
- 92
- 96
- 100
Next, let’s use the formula for the sum of an arithmetic series. The formula is:
Sum = n/2 * (first term + last term)
In this case:
- The first term (a) = 16
- The last term (l) = 100
- The number of terms (n) can be found using the formula for the number of terms in an arithmetic sequence:
n = (last term – first term)/difference + 1
Calculating the number of terms:
- Difference = 4
- n = (100 – 16)/4 + 1 = 21
Now we can substitute:
Sum = 21/2 * (16 + 100)
Sum = 21/2 * 116
Sum = 21 * 58 = 1218
Thus, the sum of all multiples of 4 from 16 to 100 is 1218.