Question 24 The 15th term of an arithmetic progression is 37, and the common difference is -2.

The n-th term of an arithmetic progression is given by the formula a_n = a + (n-1)d. By substituting the known values for the 15th term, common difference, and position, we can solve for the first term (a).

Step-by-step Derivation:
Step 1: Identify the given values from the problem statement.

• n = 15 (the 15th term)
• a_15 = 37 (the value of the 15th term)
• d = -2 (the common difference)

Step 2: Use the general formula for the n-th term of an Arithmetic Progression (AP):
a_n = a + (n - 1)d

Step 3: Substitute the known values into the formula:
37 = a + (15 - 1)(-2)

Step 4: Simplify the expression inside the parentheses:
37 = a + (14)(-2)

Step 5: Perform the multiplication:
37 = a - 28

Step 6: Isolate the first term (a) by adding 28 to both sides of the equation:
a = 37 + 28
a = 65

Conclusion: The first term of the arithmetic progression is 65.