Question

) what is the sum of all three digit even numbers divisible by seventeen?

Answer 1

To FInd:

All 3 digit even number divisible  by 17.

Explanation:

To be even and divisible by 17, the number must be a multiple of (2 x 17 = 34)

Solution:

Find the smallest 3 digit even number divisible by 34:

Smallest number = 100

100 ÷ 34 = 2 Remainder 32

Smallest number divisible by 34 = 100 + (34 - 32)

Smallest number divisible by 34 = 102

Find the biggest 3 digit even number divisible by 34:

Biggest number = 999

999 ÷ 34 = 29 Remainder 13

Biggest number divisible by 34 = 29 x 34

Biggest number divisible by 34 = 986

Find the number of terms:

Tn = a + (n - 1)d

986 = 102 + (n - 1)(34)

986 = 102 + 34n - 34

986 = 34n + 68

34n = 918

n = 27

Find the sum of these 27 terms:

Sn = n/2 ( a1 + an)

Sn = 27/2 ( 102 + 986)

Sn = 14688

Answer: The sum of all 3 digit even numbers divisible by 17 is 14688

Answer 2

$\large\underline\mathrm{Solution}$

The smallest 3 digit even number division by 34:

Smallest number = 100

$\implies$ 100/2 = 2 remainder 32

The biggest number divisible by 34.

Biggest number = 999

$\implies$ 999/34 = 29 remainder 13

Biggest number divisible by 34 = 29 × 34

$\implies$ 34 = 986

Find the number of terms.

Tn = a + (n - 1)d

$\implies$ 986 = 102 + (n - 1)(34)

$\implies$ 986 = 102 + 34n - 34

$\implies$ 986 = 34n + 68

$\implies$ 34 = 918

$\implies$ n = 27

Find the sum of 27th .

$\implies$ Sn = n/2 (a1 + an)

$\implies$ Sn = 27/2 (102 + 986)

$\implies$ Sn = 14688.