Question

30 POINTS. Ally is given three different sums of the same sequence to calculate. If she completes the three problems in order do the sums increase or decrease in value. Why?

A) The sums decrease in value because you are subtracting.

B) The sums increase in value because even though you are multiplying and adding. There is no subtraction or division.

C) The sums increase in value because even though you subtract 7 from each term you are still increasing the positive number that is being multiplied so they will increase.

D) The sums decrease in value because even though you are increasing the positive number that is being multiplied you have to subtract 7 from each answer so they will decrease.

Answer 1

Option B is correct; the sums of a sequence increase in value when only addition and multiplication of positive numbers are involved, as there is no subtraction or division to decrease the value.

Step-by-step explanation:

The question asks if the sums of a sequence increase or decrease in value as Ally calculates different sums of this sequence. The answer depends on the operations being applied to the sequence. When considering the addition and multiplication of numbers, the following rules apply:

• When two positive numbers add, the sum is positive (e.g., 3 + 2 = 5).
• When two positive numbers multiply, the product is positive (e.g., 2 x 3 = 6).
• When two numbers having opposite signs are added, the larger magnitude determines the sign and we subtract the smaller number from the larger (e.g., -5 + 3 = -2).
• In subtraction, like 5 - 3, we change the sign of the number being subtracted and then add, so 5 - 3 becomes 5 + (-3) = 2.

Using these rules, we can discern that if we are not subtracting or dividing, and only adding and multiplying positive numbers, the sums would increase in value. Therefore, option B is correct: The sums increase in value because even though you are multiplying and adding, there is no subtraction or division.