Question

In an A.P 16,14,12,.... , the sum of how many terms is 60 ? why we get double answer ? explain ?​

Answer 1

Step-by-step explanation:

We know that Sn = n/2(2a+(n-1)d)

60 = n/2(2*16+(n-1)(-2))

120 = n(34 - 2n)

120 = 34n-2n^2

n^2 -17n+60=0

n^2 -12n-5n+60=0

n=5 or 12.

Here, we get 2 answers because of a quadratic equation giving both +ve values.

Answer 2

A.P is 16, 14, 12....
therefore a = 16
D= 14-16
= -2
Sn = 60
Sn = n/2 [ 2a+( n-1)d]

Sn = n/2 [2 * 16 + (n-1) -2]
60 = n/2[ 32 -2n + 2]
60 = n/2[ 34 -2n]
60 = n/2 * 2 [ 17-n]
60 = n[17-n]
60 = 17n -n2
n2 - 17n + 60 = 0

After factorising....

n = 5 or n = 12
We get double answer because the a.p is decreasing and hence some terms get eliminated.
Thus we have double answer .