Q&A for How to Find Any Term of an Arithmetic Sequence

Subtract the 10th term from the 15th term and divide by 5: that gives you D, the difference between any two consecutive terms. Multiply D by 9, and subtract that amount from the 10th term; that gives you the first term.

This is not an arithmetic sequence. Look up geometric sequences for whatever formula you're interested in.

Subtract 8 from 100 = 92. Divide 92 by 4 (because with five terms there will be four intervals between the first and last term). That gives you 23, the size of each interval. So the sequence begins with 8 and has a common difference of 23.

Common difference (d) = 4 - 7 = -3. First term (a) = 7. Given term (t) = -38. t = a + (n - 1) d, or, -38 = 7 + (n-1) -3. Therefore, n=16, which implies -38 is the 16th term.

Starting with n = 1, the first three terms are 7, 11, and 15.

This is a geometric progression, where each term is calculated by the previous one multiplied by a certain constant. In the example, the constant (q) is 2, because 2 * (1/2) = 1, 2 * 1 = 2, 2 * 2 = 4 .... The formula is: an = a1 x q^(n-1); in the example: an = 1/2 x 2^(n-1). The 10th term, for example, is: a(10) = 1/2 x 2^(9) = 256.

See Method 3 above, particularly Step 3.

The formula for the nth term a(n) is given in Method 3 above. Plug in your numbers and solve for n.

To find the "nth" term of an arithmetic sequence, start with the first term, a(1). Add to that the product of "n-1" and "d" (the difference between any two consecutive terms). For example, take the arithmetic sequence 3, 9, 15, 21, 27.... a(1) = 3. d = 6 (because the difference between consecutive terms is always 6. Say you want to find the seventh term in the sequence (n = 7). Then a(7) = a(1) + (n-1)(d) = 3 + (6)(6) = 39. 39 is the seventh term in this sequence.

Say you have the 4th, 5th, and 6th term in the sequence, for example, 6, 8, 10. The formula for finding any term in the sequence is Un (or Ur) = the 1st term + the term you are trying to find minus 1 (if you were finding the 5th term it would be 5 -1) x d (the common difference). Since you already have some of the sequence, you can plug in the terms you have into the formula and solve to find the first term: U(4) = 6 = U(1) + (4-1)2. The fourth term, U(4) was given as 6 and the common difference is 2. After simplifying, the formula looks like this: 6 = U(1) + 6. After subtracting 6 from both sides, you get that U(1) is equal to 0, and you can now use this to find any other term in the sequence.

Subtract any term in the sequence from the term that follows it. If you don't know any two consecutive terms, solve for "d" in one of the equations given in the above article, assuming you know the other values shown in the equation. There are several other wikiHow articles pertaining to arithmetic sequences, and they show other formulas that might help you find "d."

Because that series is neither an arithmetic nor a geometric sequence, there is no formula for the sum of the series and no way to answer your question.

You would also have to know at least one of the terms of the sequence and which term it is (first, second, third, etc.). Then you would construct the sequence forward and/or backward from the given term(s).

First let's find d, then everything else will be easy. To get from the 3rd term to the 10th, we added the common difference 10-3 or 7 times. That is, 40 = 12 + 7d; so 28 = 7d and d = 4. Then, by the same reasoning, u(1) = 12 - 2d = 12 - 2*4 = 4; u(100) = 40 + 90d = 40 + 90*4 = 40+360 = 400. And generally, u(n) = 4n.

You cannot find the 7th term unless you know the first term and second term. This is because you need to use the value that equals to the second term - the first term. Also, you need to know whether this is a geometric sequence or an algebraic one.

That is neither an arithmetic nor a geometric sequence, so you can't find a given term.

Use the formula in the above article for the nth term of an arithmetic sequence: a(n) = a(1) + (n - 1) d. Here n = 20, a(1) = 126, and d = -13. a(20) = 126 + (20 - 1)(-13) = 126 + (19)(-13) = 126 - 247 = -121. That's the 20th term.

Add x to each succeeding term. The second through fifth terms are (8 + x), (8 + x + x) or (8 + 2x), (8 + 3x) and (8 + 4x).

The "nth" term is "n," so the 6th term is 6.