How many terms of an AP 48, 42, 36.... be taken so that the sum is 216? Explain the double answer.
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use formula of sum of n terms
Sn=n/2 {2a+(n-1) d}
216=n/2 {2 x 48 +(n-1)(-6)
216=n (48 -3n+3)
216=51n-3n^2
72=17n-n^2
n^2-17n+72=0
due to quadratic equation we solve gain two solution
now,
n^2-9n-8n+72=0
(n-8)(n-9)=0
n=8,9
tn=a+(n-1) d
48+(8-1)(-6)=6
t9=48+(9-1)(-6)
=48-48=0
hence we see nth term is zero it means adding of 9th term isn't change of value of sum this reason n gain two value.
so, n=8 and 9 both are correct in this series
Sn=n/2 {2a+(n-1) d}
216=n/2 {2 x 48 +(n-1)(-6)
216=n (48 -3n+3)
216=51n-3n^2
72=17n-n^2
n^2-17n+72=0
due to quadratic equation we solve gain two solution
now,
n^2-9n-8n+72=0
(n-8)(n-9)=0
n=8,9
tn=a+(n-1) d
48+(8-1)(-6)=6
t9=48+(9-1)(-6)
=48-48=0
hence we see nth term is zero it means adding of 9th term isn't change of value of sum this reason n gain two value.
so, n=8 and 9 both are correct in this series
abhi178:
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