## Subject 2.

Consider the sequence of natural numbers $1,2,3,5,6,7,9,10,11,13,14, \ldots$

a. Find how many numbers less than 100 are in the sequence.

b. Find the sum of the numbers less than 100 in the sequence.
## Subject 2.

a. The sequence is formed by the natural numbers from which the multiples of 4 have been removed ...1p. From 1 to 100 (inclusive) there are 25 multiples of 4 ...1p. $100-25=75$ numbers less than 100 are in the sequence. ...1p.

b. $1+2+3+\ldots+100=5050$ ...1p.

$4+8+12+\ldots+100=4(1+2+3+\ldots+25)=1300$ ...2p.

Finalization $S=5050-1300=3750$ ..1p.