Integers - ACT Math

Use the formula _a_n = _a_1 + (n – 1)d

_a_6 = a_1 + 5_d

_a_9 = a_1 + 8_d

Subtracting these equations yields

_a_6 – a_9 = –3_d

–7 – 8 = –3_d_

d = 5

_a_1 = 33

Then use the formula for the series; = –30

The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.

The sequence is multiplied by each time.

The formula for finding the term of an arithmetic sequence is as follows:

where

= the difference between consecutive terms

= the number of terms

Therefore, to find the term:

Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is or . The second is or , and so forth... Therefore, for the th element, the value will be or .

Notice that between each of these numbers, there is a difference of ; however the first number is , the second , and so forth. This means that for each element, you know that the value must be , where is that number's place in the sequence. Thus, for the rd element, you know that the value will be or .

If Steve has 10 chores, Jeff has 7 chores (3 less than Steve). Tom has twice as many as Steve, so Tom has 14 chores.

Create an equation for the situation described and solve:

Create an equation to decribe the above situation and solve.

Total presents given out is represented by .

Presents given to Sally is represented by .

Presents given to Billy is represented by .

Thus our equation becomes,

Always start by gathering your facts. You know that if is odd, then neither of those numbers are even. (If either were, then the product would be even.) Now, the rules for subtracting are just like adding. If the difference of two numbers is even, then they must either both be odd or both be even. Thus if is even and we know that is odd, then we know that must be odd. Thus if is odd, it is also true that is even, for both and are even.

Solve each equation for , plot on number line.

The integer halfway between –4 and 18 is 7. The number 7 is 11 greater than –4 and 11 less than 18. Another way to determine this would be to find the average of the two numbers: (–4 + 18)/2 = 14/2 = 7.

The answer here relies on knowledge of how numbers are arranged on a number line. We are looking for the number furthest from –3. The number furthest from –3 can lie either to the left of –3 which would be negative numbers that are more negative, or further from 0 than –3. The number furthest from –3 could also lie to its right on the number line, these numbers include all negative numbers between –3 and 0,0, and all positive numbers. The number that satisifes these conditions and is the furthest from –3 on the number line is –8

To find distance between two points, take the second and subtract the first.

So 7–(–6) = 7 + 6 = 13

The distance between 2 numbers on a number line is the sum of their absolute values.

Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.

Starting at and adding is the same as subtracting . .

Starting at and adding is the same as subtracting . .

Adding to is the same as subtracting from . .

The 4 consecutive of integers greater than 9 (but not including 9) are 11, 13, 15, 17. Added together, we get 56.