The sum of how many in the series 39,33,27 ... will be 144? Give reasons for two answers.
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a=54
d=51−54=−3
S
n
=513
S
n
=
2
n
[2a+(n−1)d]
⇒513=
2
n
[2(54)+(n−1)(−3)]
⇒1026=n[108−3n+3]
⇒1026=n[111−3n]
⇒3n
2
−111n+1026=0
⇒n
2
−37n+342=0
⇒n
2
−18n−19n+342=0
⇒(n−18)(n−19)=0
⇒n=18,19
T
18
=a+17d=54+17(−3)=3
T
19
=a+18d=54+18(−3)=0
Since the 19
th
term is 0, therefore no change will be seen in the sum of 18 and 19 terms. That is the reason why we are getting 2 ans
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