In the following arithmetic sequence, what is the value of m?
-2, 4, m, 16 . . .
Anonymous = Unknown
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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