Final answer:
To find the value of m in the sequence 25, m+1, 35, calculate the common difference and solve for m by setting the second term equal to the first term plus the common difference.
Step-by-step explanation:
Finding the Value of m in an Arithmetic Sequence
To determine the value of m in the arithmetic sequence 25, m+1, 35, first we must understand that the common difference (d) is the same between each term. To find d, subtract the first term from the third term and then divide by 2 because m+1 is the second term and should therefore be exactly one common difference away from each of the others.
d = (35 - 25) / 2 = 10 / 2 = 5
Now, using the common difference, we add it to the first term to find the second term (which involves m):
25 + d = m + 1
Substitute the value of d into the equation:
25 + 5 = m + 1
30 = m + 1
This yields the solution for m:
m = 30 - 1
m = 29
Thus, the value of m in the given arithmetic sequence is 29.