If the first term of an arithmetic progression is 7 and the last term is 37, with a total of 16 terms, what is the common difference?

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Q: If the first term of an arithmetic progression is 7 and the last term is 37, with a total of 16 terms, what is the common difference?

Solution: Using the formula for the last term, l = a + (n-1)d, we have 37 = 7 + (16-1)d. Solving gives d = 2.

Steps: 10

Step 1: Identify the first term (a) of the arithmetic progression, which is given as 7.
Step 2: Identify the last term (l) of the arithmetic progression, which is given as 37.
Step 3: Identify the total number of terms (n) in the arithmetic progression, which is given as 16.
Step 4: Use the formula for the last term of an arithmetic progression: l = a + (n-1)d.
Step 5: Substitute the known values into the formula: 37 = 7 + (16-1)d.
Step 6: Simplify the equation: 37 = 7 + 15d.
Step 7: Subtract 7 from both sides to isolate the term with d: 37 - 7 = 15d.
Step 8: Calculate the left side: 30 = 15d.
Step 9: Divide both sides by 15 to solve for d: d = 30 / 15.
Step 10: Calculate the value of d: d = 2.