Login/Sign Up
Home » How many terms of the AP 20, 19 1 3 , 18 2 3 must be taken to make the sum 300? Explain the double answer.
How many terms of the AP 20, 19 1 3 , 18 2 3 must be taken to make the sum 300? Explain the double answer.
RS aggarwal class 11 Maths Arithmetic progressions
How many terms of the AP 20, 19 1 3 , 18 2 3 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

⇒ 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 an – 1>an,it is bound to have negative values in the series. Sn is maximum for n = 30 or n = 31(S30 = S31 = Smax = 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.
.

i

More Material