Question

the sum of three consecutive even number is 60 . find the smaller number
answer it step by step​

Answer 1

Answer:

Let 2n = the smallest consecutive even number.

Let 2(n + 1) = 2n + 2 = the next consecutive even number, and ...

Let 2(n + 2) = 2n + 4 = the third consecutive even number.

Since the sum of these 3 consecutive even numbers is 60, we can write the following equation:

2n + (2n + 2) + (2n + 4) = 60

2n + 2n + 2 + 2n + 4 = 60

By the Commutative Property of Addition, i.e., a + b = b + a, we have on the left side of the equation:

2n + 2n + 2n + 2 + 4 = 60

Now, collecting like-terms on the left side, we get:

(2 + 2 + 2)n + 6 = 60

(6)n + 6 = 60

6n + 6 = 60

Now, in order to solve for n, we begin isolating n on the left side of the equation by subtracting 6 from both sides:

6n + 6 - 6 = 60 - 6

Step-by-step explanation:

Answer 2

Let the first even number be a .

So, the 3 consecutive numbers will be a , a+2 , a+4

Sum of the 3 consecutive even numbers = 60

So here a , a+2 , a+4 form an A.P.

therefore, here first term(A) = a

difference (d) = a+2 - a

                   d=2

and Sn = 60

we know Sn = n/2 * 2a + {n-1}d

putting the values

Sn = 3/2 * 2a + 4                   [sn=60]

60 = 3/2 * 2a + 4

120 = 3 * 2a +4

40-4 = 2a

36 = 2a

a= 18

So the smaller number is 18