# 13. The sum of the squares of three consecutive positive integers is 770. What is the largest
of these integers?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19

The largest  of these integers is 17T

Let the 3 consecutive positive integers be x-1, x and x + 1

If the sum of the squares of three consecutive positive integers is 77, then;

Expand

x²-2x+1 + x²+x²+2x+1 = 770

3x²+2 = 770

3x² = 750

x² = 250

x = 16

Largest number = 16 + 1 = 17

Hence the largest  of these integers is 17

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Step-by-step explanation:

The three consecutive numbers are 15 16 and 17 because when you find out the squares 15 = 225 16 = 256 17 = 289

Now add these numbers 225 + 256 +289 = 770

So the largest is 17 C option

10 - 8 = -2

  8 - 6 = -2

etc, so -2 is the common difference

step-by-step explanation: