(x - d) + x + (x + d) = 12 --> Create an equation using the first piece of information - "Three consecutive terms... have a sum of 12"
x - d + x + x + d = 12 --> Simplify the left side of this equation (d cancels out)
3x = 12 --> Divide both sides by 3
<u>x = 4
</u>
Use the value of x (x = 4) to find the value of d. To do this, set up another equation using the second piece of information.
(x - d) * (x + d) * x = - 80 --> "Three consecutive terms... have... a product of -80". Then, substitute the value of x (4) into this equation.
(4 - d) * (4 + d) * 4 = - 80 --> Multiply out the sets of brackets, the * 4 is dealt with afterwards
4(16 - 4d + 4d - d²) = - 80 --> Simplify the expression inside the brackets
4(16 - d²) = - 80 --> Multiply out these brackets by the 4
64 - 4d² = - 80 --> Subtract 64 from both sides
- 4d² = - 144 --> Divide both sides by - 4
d² = 36 --> Square root both sides
<u>d = 6
</u>Now, find the values of the terms of the sequence by using substituting the values of x and d into the expressions given.
<u>
</u><u />1. x - d = 4 - 6 = <u>- 2
</u><u></u>2.<u> x = 4</u>
3. x + d = 4 + 6 = <u>10
</u>
The three terms are - 2, 4, 10.
<u>
</u>
Note
16 cups = 1 gallon (US)
or
18.2 cups = 1 gallon (UK)
We shall use the US gallon for the calculation, therefore
1 gallon = 16 cups.
Answer: 16
Answer:
114
Step-by-step explanation:
15 x 2 + 9 x 2 + 11 x 3 + 11 x 3 = 114
(the bottom portion is equal to 3 x 11)
