What is the sum of the first 10 terms of an arithmetic progression whose first term is 5 and last term is 32?

The sum of the first 10 terms of the arithmetic progression is 185.

According to the provided reference, the sum of the first 10 terms of an arithmetic progression (AP) with a first term of 5 and a tenth term (last term in this case) of 32 is 185. This can be calculated using the formula for the sum of an arithmetic series.

Here's a breakdown:

• Understanding Arithmetic Progressions (AP): An AP is a sequence of numbers where the difference between any two consecutive terms is constant.
• Given Information:
  • First term (a) = 5
  • Last term (l or a₁₀) = 32
  • Number of terms (n) = 10
• Formula for the Sum of an AP: The sum (S_n) of the first 'n' terms of an AP is given by:
  S_n = (n/2) * (a + l)
  where:
  • n = number of terms
  • a = first term
  • l = last term
• Calculation:
  • S₁₀ = (10/2) * (5 + 32)
  • S₁₀ = 5 * 37
  • S₁₀ = 185

Therefore, the sum of the first 10 terms of the given arithmetic progression is indeed 185.