The fourth term of this sequence will be 5m + 2m = 7m. If we add up the first four terms, we get m + 3m + 5m + 7m = 4m + 12m = 16m. Since m is an integer, the sum of the first four terms, 16m, will have a factor of 16. Looking at the answer choices, 60 is the only answer where 16 is not a factor, so that is the correct choice.

Let d represent the common difference between consecutive terms.

Let a_n denote the nth term in the sequence. 

In order to get from the tenth term to the twentieth term in the sequence, we must add d ten times.

Thus a_{20 =} a₁₀ + 10d

20 = 40 + 10d

d = -2

In order to get from the first term to the tenth term, we must add d nine times.

Thus a_{10 =} a_{1 +} 9d

40 = a₁ + 9(-2)

The first term of the sequence must be 58.

Our sequence looks like this: 58,56,54,52,50…

We are asked to find the nth term such that the sum of the first n numbers in the sequence equals 0.

58 + 56 + 54 + …. a_{n =} 0

Eventually our sequence will reach zero, after which the terms will become the negative values of previous terms in the sequence.

58 + 56 + 54 + … 6 + 4 + 2 + 0 + -2 + -4 + -6 +….-54 + -56 + -58 = 0

The sum of the term that equals -2 and the term that equals 2 will be zero. The sum of the term that equals -4 and the term that equals 4 will also be zero, and so on.

So, once we add -58 to all of the previous numbers that have been added before, all of the positive terms will cancel, and we will have a sum of zero. Thus, we need to find what number -58 is in our sequence.

It is helpful to remember that a_n = a₁ + d(n-1), because we must add d to a₁ exactly n-1 times in order to give us a_n. For example, a₅ = a₁ + 4d, because if we add d four times to the first term, we will get the fifth term. We can use this formula to find n.

-58 = a_n = a₁ + d(n-1)

-58 = 58 + (-2)(n-1)

n = 59

We can see how the sequence begins by writing out the first few terms:

1, –2, 4, –8, 16, –32, 64, –128.

Notice that every other term (of which there are exactly 50/2 = 25) is negative and therefore less than 25. Also notice that after the fourth term, every term is greater in absolute value than 5, so we just have to find the number of positive terms before the fourth term that are less than 5 and add that number to 25 (the number of negative terms in the first 50 terms).

Of the first four terms, there are only two that are less than 5 (i.e. 1 and 4), so we include these two numbers in our count: 25 negative numbers plus an additional 2 positive numbers are less than 5, so 27 of the first 50 terms of the sequence are less than 5.

Look for cancellations to simplify.  The sum of all consecutive integers from  to  is equal to . Therefore, we must go a little farther.  , so the last number in the sequence in .  That gives us  negative integers,  positive integers, and don't forget zero! .

If Brad can walk 3600 feet in 10 minutes, then he can walk 3600/10 = 360 feet per minute, and 360/60 = 6 feet per second.

There are 3 feet in a yard, so Brad can walk 6/3 = 2 yards per second, or 2 x 10 = 20 yards in 10 seconds.

The simplest way to handle this question is to consider the sequence as being a set of 3 repeating terms, (3,2,4). Within the first 18 terms in the sequence, this pattern will repeat a total of 6 times.

The sum of one repeat is:

Since there are 6 repeats, take the sum of one repeat (9) and multiply by the number of repeats:

The sum of the first 18 terms is 54.

Shortcut:  If you add up al the integers from  to , the sum is zero because

the positives and negatives all cancel out.  Start with the next number:

We start by multiplying 6 times 46, since the first 4 terms are already listed. We then add the product, 276, to the last listed term, 20. This gives us our answer of 296.

All answers in the sequence must end in a 5 or a 0.

Let a₁ represent the first term of the sequence and a_n represent the nth term.

We are told that each term is two greater than the term that precedes it. Thus, we can say that:

a₂ = a₁ + 2

a₃ = a₁ + 2 + 2 = a₁ + 2(2)

a₄ = a₁ + 3(2)

a₅ = a₁ + 4(2)

a_n = a₁ + (n-1)(2)

The problem tells us that the sum of the first five terms is equal to the difference between the fifth and first terms. Let's write an expression for the sum of the first five terms.

sum = a₁ + (a₁ + 2) + (a₁ + 2(2)) + (a₁ + 3(2)) + (a₁ + 4(2))

= 5a₁ + 2 + 4 + 6 + 8

= 5a₁ + 20

Next, we want to write an expression for the difference between the fifth and first terms.

a₅ - a₁ = a₁ + 4(2) – a₁ = 8

Now, we set the two expressions equal and solve for a₁.

5a₁ + 20 = 8

Subtract 20 from both sides.

5a₁ = –12

a₁ = –2.4.

The question ultimately asks us for the tenth term of the sequence. Now, that we  have the first term, we can find the tenth term.

a₁₀ = a₁ + (10 – 1)(2)

a₁₀ = –2.4 + 9(2)

= 15.6

The answer is 15.6 .