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Learn to write expressions for tables and sequences. Additional Example 1: Writing an Expression. Write an expression for the missing value in the table. Rusty’s age is Spike’s age plus 4. Spike’s Age. Rusty’s Age. 2 + 4 = 6. 2. 6. 3. 7. 3 + 4 = 7. 4 + 4 = 8. 4. 8. a.
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Additional Example 1: Writing an Expression Write an expression for the missing value in the table. Rusty’s age is Spike’s age plus 4. Spike’s Age Rusty’s Age 2 + 4 = 6 2 6 3 7 3 + 4 = 7 4 + 4 = 8 4 8 a a + 4 a + 4 When Spike’s age is a, Rusty’s age is a + 4.
Check It Out: Example 1 Write an expression for the missing value in the table. Ty’s Age Rich’s Age Rich’s age is Ty’s age times 7. 1 7 = 7 1 7 2 14 2 7 = 14 3 7 = 21 3 21 a a 7 a 7 When Ty’s age is a, Rich’s age is a 7 or 7a.
Additional Example 2: Writing an Expression for a Sequence Write an expression for the sequence in the table. Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check. Guess 7nGuess 3n + 4 Check by substituting 2. Check by substituting 2. 7 • 2 does not equal 10. 3 • 2 + 4 = 10. The expression 3n + 4 works for the entire sequence. 3 • 1 + 4 = 7, 3 • 2 + 4 = 10, 3 • 3 + 4 = 13, 3 • 4 + 4 = 16 The expression for the sequence is 3n + 4.
Check It Out: Example 2 Write an expression for the sequence in the table. Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check. Guess 7nGuess 5n + 2 Check by substituting 2. Check by substituting 2. 7 • 2 does not equal 12. 5 • 2 + 2 = 12. The expression 5n + 2 works for the entire sequence. 5 • 1 + 2 = 7, 5 • 2 + 2 = 12, 5 • 3 + 2 = 17, 5 • 4 + 2 = 22 The expression for the sequence is 5n + 2.
In each row of the table, the area is half the product of the base and the height. The expression is or 3h. 6h __ 2 Additional Example 3: Writing an Expressions for the Area of a Figure A triangle has a base of 6 inches. The table shows the area of the triangle for different heights. Write an expression that can be used to find the area of the triangle when its height is h inches. 6 • 1 = 6, 6 ÷ 2 = 3 6 • 2 = 12, 12 ÷ 2 = 6 6 • 4 = 18, 18 ÷ 2 = 9 3h
In each row of the table, the area is half the product of the base and the height. The expression is or 2h. 4h __ 2 Check It Out: Example 3 A triangle has a base of 4 inches. The table shows the area of the triangle for different heights. Write an expression that can be used to find the area of the triangle when its height is h inches. 4 • 3 = 12, 12 ÷ 2 = 6 4 • 4 = 16, 16 ÷ 2 = 8 4 • 5 = 20, 20 ÷ 2 = 10 2h