If the first term of an arithmetic sequence is 2 and the 7th term is 3278, what is the common difference?

using the standard terminology....

a = 2
t(7) = a+6d
2 + 6d = 3278
6d = 3276
d = 546

To find the common difference of an arithmetic sequence, we can use the formula for the nth term:

a_n = a_1 + (n-1)d

where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference.

We are given that the first term, a_1, is 2 and the 7th term, a_7, is 3278. Let's substitute these values into the formula:

3278 = 2 + (7-1)d

Simplifying the equation gives:

3278 = 2 + 6d

Next, let's isolate the d term by subtracting 2 from both sides of the equation:

3278 - 2 = 6d

3276 = 6d

Finally, divide both sides of the equation by 6 to solve for d:

d = 3276 / 6

Simplifying the expression gives:

d = 546

Therefore, the common difference of the arithmetic sequence is 546.

To find the common difference of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:

nth term = a + (n - 1) * d

where "nth term" is the term number, "a" is the first term, "n" is the number of the term, and "d" is the common difference.

In this case, we are given the first term (a = 2) and the 7th term (n = 7), and we need to find the common difference (d).

Let's substitute these values into the formula and solve for the common difference:

3278 = 2 + (7 - 1) * d

Simplifying the equation:

3278 = 2 + 6d

Now, we can subtract 2 from both sides:

3278 - 2 = 6d

3276 = 6d

To isolate "d," we can divide both sides by 6:

3276/6 = d

d ≈ 546

Therefore, the common difference of the arithmetic sequence is approximately 546.