In the following arithmetic sequence, what is the value of m?

-2, 4, m, 16 . . .

Anonymous = Unknown

Why did you post the question and answer?

To find the value of m in the given arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

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

In the given sequence, we know that a_1 = -2 and d = 4 - (-2) = 6.

Let's find the position of the term m in the sequence. We can count the number of terms between the first term (-2) and the third term (m) to determine the position.

The number of terms between two terms can be calculated using the formula:

n = (a_n - a_1) / d + 1

Let's substitute the known values into the formula:

n = (m - (-2)) / 6 + 1

Now, let's determine the value of n by counting the terms between -2 and m. In the given sequence, we have one term between -2 and 4, so n = 2.

Now that we know n, we can substitute the values into the formula for the nth term:

a_n = a_1 + (n-1)d

m = -2 + (2-1) * 6

m = -2 + 6

m = 4

Therefore, the value of m in the given arithmetic sequence is 4.

The correct answer is 10.

The difference from -2 to 4 is 6,so 4+6=10
10+6=16

m=10