first term of the arithmetic sequence is 13. two other terms of the sequence are 37 and 73. common difference is consecutive terms integers. determine all possible values for 100th term.

after this, if you want help on more of these sequence problems, how about showing where you get stuck, or the answer you want to confirm?

If you are trying to say that the commons difference is an integer, then we know it is positive, and divides 73-37=36

so, the difference may be 1,2,3,4,6,9,12,18

However, d must also divide 37-13=24
and 73-13=60

That narrows our choices to 1,2,3,4,6,12

d T100
1 13+1*99=112
2 13+2*99=211
3 and so on
4
6
12

thank you

Well, well, well! Looks like we have an arithmetic sequence here, trying to play a little game of hide and seek. Let's join in on the fun!

We know that the first term is 13. Now, let's try to find the common difference. Here's a little math joke for you: why did the math book look so sad? Because it had too many problems! But don't worry, I'm here to help.

To find the common difference, we can subtract the first term from the second term. So, 37 minus 13 is 24. Now, let's see if the third term follows this pattern. 73 minus 37 is also 36. Well, well, well! Looks like we might have found our sneaky little common difference.

Now, to find the 100th term, we can use a formula: n-th term = first term + (n - 1) * common difference. In this case, the first term is 13 and the common difference seems to be either 24 or 36.

So, let's do some calculations. If the common difference is 24, then the 100th term will be 13 + (100 - 1) * 24 = 2413. Pretty neat!

But wait! If we try the other possible common difference, 36, we get 13 + (100 - 1) * 36 = 3377. Oh my, oh my, looks like we have another possible answer!

So, all possible values for the 100th term are 2413 and 3377. Now, let's celebrate our victory with a little math party! Who's in?

To find the 100th term of the arithmetic sequence, we need to determine the common difference first.

We know that the first term is 13. Let's find the common difference using the second and third terms of the sequence (37 and 73).

The common difference (d) can be calculated by subtracting the second term from the first term (d = a2 - a1) or the third term from the second term (d = a3 - a2).

Using the second term:
d = a2 - a1
d = 37 - 13
d = 24

Using the third term:
d = a3 - a2
d = 73 - 37
d = 36

Since the difference between consecutive terms is an integer, the possible values for the common difference are 24 and 36.

Now, we can find the 100th term using the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * d

For d = 24:
a100 = 13 + (100 - 1) * 24
a100 = 13 + 99 * 24
a100 = 13 + 2376
a100 = 2389

For d = 36:
a100 = 13 + (100 - 1) * 36
a100 = 13 + 99 * 36
a100 = 13 + 3564
a100 = 3577

Therefore, the possible values for the 100th term of the arithmetic sequence are 2389 and 3577.

To determine the possible values for the 100th term of the arithmetic sequence, we first need to find the common difference of the sequence. Since the common difference is consecutive terms of integers, we can subtract the second term from the first term and the third term from the second term to find the common difference.

Common difference (d) = Second term - First term = 37 - 13 = 24
Common difference (d) = Third term - Second term = 73 - 37 = 36

Since the common difference is consecutive terms integers, it must be a positive or negative whole number. Therefore, the possible values for the common difference are 24 and -24, 36 and -36.

Now, to find the 100th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n - 1) * common difference

Substituting the given values:

For d = 24:
100th term = 13 + (100 - 1) * 24 = 13 + 99 * 24 = 2497

For d = -24:
100th term = 13 + (100 - 1) * (-24) = 13 + 99 * (-24) = -2387

For d = 36:
100th term = 13 + (100 - 1) * 36 = 13 + 99 * 36 = 3589

For d = -36:
100th term = 13 + (100 - 1) * (-36) = 13 + 99 * (-36) = -3467

Therefore, the possible values for the 100th term of the arithmetic sequence are 2497, -2387, 3589, and -3467.