Question

Find the sum of all multiples of 2 or 3 between 1 and 51

Answer 1

Answer:

2×1 = 2 and 2×51=102

3×1 = 3 and 3×51=153

Answer 2

The sum of all multiples of 2 or 3 between 1 and 51 = 216

Step-by-step explanation:

The all multiples of 2 or 3 between 1 and 51 ( multipe of 6):

6, 12, 18, 24, 30 , 36, 42, 48

The given sequence are in AP.

Here, first term(a) = 6, common difference(d) = 12 - 6 = 6 and last term (l) = 48

To find, the sum of all multiples of 2 or 3 between 1 and 51 = ?

Let n be the number of terms.

$a_{n} =a+(n-1)d$

⇒ 6 + (n - 1)6 = 48

⇒ (n - 1)6 = 48 - 6 = 42

⇒ n - 1 = 7

⇒ n = 8

We know that,

The sum of nth terms of an AP

$S_{n}=\dfrac{n}{2}(a+l)$

$=\dfrac{8}{2}(6+48)$

$=4\times 54$

= 216

Thus, the sum of all multiples of 2 or 3 between 1 and 51 = 216