What is the formula for the sum of an arithmetic progression with n terms, first term a1 and last term an?

• A. n*(a1+an)/2
• B. n*a1 + an
• C. (a1+an)/2
• D. n*(a1+an)

Answer: (A)

In an arithmetic progression, you can find the sum by using the average of the terms times how many terms you have. The average value of all terms is (a1 + an) / 2, since the sequence increases by a constant step. Multiply that average by the number of terms n to get the total: S_n = n * (a1 + an) / 2, which is the same as n/2 times (a1 + an). A quick way to see why this works is to pair terms from the ends: each pair sums to a1 + an, and there are n/2 such pairs (for odd n, the middle term equals the average, so the same result holds). The other options either miss the division by 2, or simply give the average rather than the total sum.