Question

Find the sum of all positive integers less than 200, which:

Answer 1

Answer:

3900

Step-by-step explanation:

We want the sum from 5 to 195

5, 10, 15, 20,......195

an = 5 + 5(n-1)  since we can write this as an arithmetic sequence, adding 5 each time

The sum of the terms of an arithmetic sequence is given by

Sn = n/2 [2a1 + (n - 1)d],  

where d is the common difference of 5 and n is the term we want to add to

195/5 = 39  so it is the 39th term

s39 =39/2 [2*5 + (39-1)*5)]

s38 = 19.5[10+38*5]

        =19.5*[10+190]

          19.5*200

          =3900