2 1 CONSECUTIVE NUMBERS ALGEBRA I CONSECUTIVE INTEGERS

2. 1 CONSECUTIVE NUMBERS ALGEBRA I

CONSECUTIVE INTEGERS • Examples n are numbers in counting orders -3, -2, -1, 0, 1, 2, 3 ---|-----|------|-----|-----|-----|-----|--- -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

---|-----|------|-----|-----|-----|-----|--- -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 • When counting CONSECUTIVE integers, You will… Add by 1’s Ex + 1, + 2, + 3 • When counting CONSECUTIVE ODD OR EVEN integers, you will … Add by 2’s Ex + 2, + 4, + 6, + 8

Examples 1) The sum of two consecutive integers is 17. Find the two numbers. x = represents 1 st number x+1 = represents 2 nd number 2 x + 1 = 17 -1 -1 2 x = 16 2 2 X=8 add 1 st and 2 nd number together and set equal to 17. Solve. Now x + 0 becomes 8 + 0 which is 8 Now x +1 becomes 8 + 1 which is 9 Check 8 + 9 = 17

Examples 2) The sum of three consecutive integers is 129. Find the three numbers. x = represents 1 st number x+1 = represents 2 nd number x+2 =represents 3 rd number 3 x + 3 = 129 -3 3 x add 1 st, 2 nd & 3 rd number together and set equal to 129. Solve. -3 = 126 3 3 X=42 Now x + 0 becomes 42 + 0 which is 42 Now x +1 becomes 42 + 1 which is 43 Now x + 2 becomes 42 + 2 which is 44 Check 42 + 43 + 44 =129

Examples 3) The sum of four consecutive integers is -334. Find the four numbers. x = represents 1 st number x+1 =represents 2 nd number x+2 =represents 3 rd number x+3 = represents 4 th number 4 x + 6 = -334 add 1 st, 2 nd , 3 rd & 4 th number together and set equal to -334. Solve. -6 4 x -6 = -340 4 4 X=-85 Now x + 0 becomes -85 + 0 which is -85 Now x +1 becomes -85 + 1 which is -84 Now x + 2 becomes -85 + 2 which is -83 Now x + 3 becomes -85 + 3 which is -82 Check -85 + -84 + -83 + -82 = -334

Examples 4) The sum of three consecutive integers is 105. Find the three numbers. x =represents 1 st number x+1 = represents 2 nd number x+2 = represents 3 rd number 3 x + 3 = 105 -3 3 x add 1 st, 2 nd & 3 rd number together and set equal to 105. Solve. -3 = 102 3 3 X=34 Now x + 0 becomes 34 + 0 which is 34 Now x +1 becomes 34 + 1 which is 35 Now x + 2 becomes 34 + 2 which is 36 Check 34 + 35 + 36 = 105

Examples 5) The sum of three consecutive even integers is 396. Find the three numbers x =represents 1 st number x+2 = represents 2 nd number x+4 =represents 3 rd number 3 x + 6 = 396 -6 3 x add 1 st, 2 nd & 3 rd number together and set equal to 396. Solve. -6 = 390 3 3 X=130 Now x + 0 becomes 130 + 0 which is 130 Now x +2 becomes 130 + 2 which is 132 Now x + 4 becomes 130 + 4 which is 134 Check 130 + 132 + 134 = 396

Examples 6) The sum of four consecutive even integers is 138. Find the four numbers. x =represents 1 st number x+2 = represents 2 nd number x+4 = represents 3 rd number x+6 = represents 4 th number 4 x + 12 = 138 add these number together and set equal to 138. Solve. -12 4 x 4 -12 = 126 4 X=31. 5 No solution: Must be whole number

Examples 7) The sum of three consecutive odd integers is 285. Find the three numbers. x =represents 1 st number x+2 » represents 2 nd number x+4 » represents 3 rd number 3 x + 6 = 285 -6 3 x add 1 st, 2 nd & 3 rd number together and set equal to 285. Solve. -6 = 279 3 3 X=93 Now x + 0 Now x + 2 Now x + 4 becomes 93 + 0 which is 93 becomes 93 + 2 which is 95 becomes Check 93 + 95 + 97 = 285 93 + 4 which is 97

Examples 8) The sum of four consecutive odd integers is 0. Find the four numbers. x =represents 1 st number x+2 = represents 2 nd number x+4 = represents 3 rd number x+6 = represents 4 th number 4 x + 12 = 0 add these number together and set equal to 0. Solve. -12 4 x = -12 4 4 X=-3 Now x + 0 Now x + 2 Now x + 4 Now x + 6 Check -3 + -1 + 1 becomes +3 =0 -3 -3 + + 0 2 4 6 which is is -3 -1 1 3