Q) How many terms of the arithmetic progression 45, 39, 33, …….. must be taken so that their sum is 180? Explain the double answer.
Ans:
In AP of 45,39, 33, …….
a = 45, d = – 6,
Sum of n terms of AP, Sn = (2a + (n-1)d)
180 = (2 x 45 + (n-1)(-6))
360 = n (90 – 6 (n-1))
6n2 – 96n + 360 = 0
n2 – 16n + 60 = 0
(n – 10) (n – 6) = 0
Hence, for n = 6 and n = 10 or we can say that for sum of AP is 180 for first 6 terms and also for first 10 terms.
Reason for 2 values: We get two values of ‘n’ because 9th and 10th term values are negative and cancel out with values of 7th and 8th terms. Hence, sum of first 6 terms and sum of 10 terms are 180.