How many terms of the AP 20, must be taken to make the sum 300? Explain the double answer.

To Find: Number of terms required to make the sum of the AP 300.

Let the first term of the AP be a and the common difference be d

Here a = 20,

⇒300 × 6 = n[120 - 2(n - 1)]

⇒n[ - 2n + 122] = 6 × 300

⇒n( - n + 61) = 3 × 300

⇒n = 36 or 25

Explanation: Since the given AP is a decreasing progression where a_{n - 1}>a_n,it is bound to have negative values in the series. S_n is maximum for n = 30 or n = 31(S₃₀ = S₃₁ = S_max = 310). The sum of 300 can be attained by either adding 25 terms or 36 terms so that negative terms decrease the maximum sum to 300.