Question

find the sum of all the numbers between 100 and 301 (inclusive), which are not the multiples of 3.

Answer 1

Answer:

26934

Step-by-step explanation:

sum of all number from 100 to 301

a = 100 d = 1 last number 301

total numbers

an = a + (n-1)d

301 = 100 + (n-1)1

301 = 100 + n - 1

301 = 99 + n

n = 301 - 99

n = 202

Sn = n/2 (2a + (n-1)d)

= 202/2 (2(100) + (202-1)1)

= 101 (200 + 201)

= 101 × 401

= 40401 (1)

multiple of 3 between 100 and 301

a = 102 d = 3. last number = 300

an = a + (n-1)d

300 = 102 + (n-1)3

300 = 102 + 3n - 3

300 = 99 + 3n

3n = 300 - 99

3n = 201

n = 201/3

n = 67

sum of multiple of 3 between 100 and 301

Sn = n/2 (2a + (n-1)d)

= 67/2 (2(102) + (67-1)3)

= 67/2 (204 + 66(3))

= 67/2 (204 + 198)

= 67/2 × 402

= 67 × 201

= 13467. (2)

subtract (1) - (2)

40401 - 13467 = 26934

hope you get your answer