11 The Sum 3 Consecutive numbers. L is 27, hund the greatest number.

Question

asked Aug 18, 2024 198k views

1 Answer

Justin Levi Winter · Answer 1 · 2024-08-24T12:16:18+0000

To find the sum of three consecutive numbers, we can use the formula:

$\displaystyle\sf \text{{Sum}} = \frac{{\text{{First number}} + \text{{Last number}}}}{2} * \text{{Number of terms}}$ .

In this case, we are given that the sum of the three consecutive numbers is 27, so we have:

$\displaystyle\sf 27 = \frac{{\text{{First number}} + \text{{Last number}}}}{2} * 3$ .

Simplifying, we have:

$\displaystyle\sf 27 = \frac{{\text{{First number}} + \text{{Last number}}}}{2} * 3$ .

Multiplying both sides by 2:

$\displaystyle\sf 54 = (\text{{First number}} + \text{{Last number}}) * 3$ .

Dividing both sides by 3:

$\displaystyle\sf 18 = \text{{First number}} + \text{{Last number}}$ .

Since the numbers are consecutive, we can express the first number in terms of the last number as follows:

$\displaystyle\sf \text{{First number}} = \text{{Last number}} - 2$ .

Substituting this expression into the equation above, we get:

$\displaystyle\sf 18 = (\text{{Last number}} - 2) + \text{{Last number}}$ .

Simplifying:

$\displaystyle\sf 18 = 2 * \text{{Last number}} - 2$ .

Adding 2 to both sides:

$\displaystyle\sf 20 = 2 * \text{{Last number}}$ .

Dividing both sides by 2:

$\displaystyle\sf 10 = \text{{Last number}}$ .

Therefore, the greatest number is 10.