Question

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How many terms of the series 54,51,48,..., be taken so that their sum is
513?Explain the double answer.​
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Answer 1

Answer:

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

513= n/2 (2* 54 +(n*-3) +3)

1026= 108n - 3n^2 +3n

3n^2 -111n +1026= 0

n^2 - 37n + 342 = 0

n= 18 or n = 19

Answer 2

Answer:

hope it helps you

Step-by-step explanation:

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 answers.