A set of 5 consecutive integers has a sum of –330. What is the value of the least integer?

Answer 1

So, we will let least integer be x:

sum of 5 integers = -330

x + x-1 + x-2 + x-3 + x-4 = -330

5x - 10 = -330

5x = -330 + 10

5x = -320

x = -320/5 = -64

x = -64

Therefore, -64 is the greatest integer. So when you count back 4 times:

-68,-67,-66, -65, -64

so therefore -68 is the least integer!

Answer 2

Let n = the first consecutive number.

Let n + 1 = the second consecutive number.

Let n + 2 = the third consecutive number.

Let n + 3 = the fourth consecutive number.

Let n + 4 = the fifth consecutive number.

Since the sum of these 5 consecutive number is -330, we can write the following equation:

n + (n + 1) + (n + 2) + (n + 3) + (n + 4) = -330

n + n + 1 + n + 2 + n + 3 + n + 4 = -330

Collecting like-terms on the left side, we have:

5n + 10 = -330...

Subtract 10 on both sides:

5n = -330 -10

5n = -340

Divide by 5 on both side

n = - 68

Therefore:

n + 1 = -68 + 1= -67

n + 2 = -68 + 2 = -66

n + 3 = -68 + 3 = -65

n + 4 = -68 + 4 = -64

The smallest integer is -68