Site icon Noon Academy

How many terms of the AP 18 16, 14, 12, …. are needed to give the sum 78? Explain the double answer.

Explanation: Since the given AP is a decreasing progression where an – 1>an,it is bound
to have negative values in the series. Sn is maximum for n = 9 or n = 10 since T10 is
0(S10 = S9 = Smax = 90). The sum of 78 can be attained by either adding 6 terms or 13
terms so that negative terms from T11 onward decrease the maximum sum to 78.