how many term of the series 54,51,48,... be taken so that their sum is 513?explain
saloni2522:
hi priyanshu. I am saloni. shefalee must have told about me??? yes or no???,
Answers
Answered by
8
Hey there! Here is the solution to your question...
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a = 54 d = -3 and Sn = 513
So, Sn = n/2 [2a + (n-1) d ]
1026 = n [ 108 + (n-1) (-3) ]
1026 = n [ 108 -3n + 3]
1026 = n [ 111 -3n]
1026 = 111n - 3n²
3n² - 111n + 1026 = 0
n² - 37n + 342 = 0 {DIVISION BY 3}
On Splitting we have:
n² - 19n - 18n + 342 = 0
n(n-19) - 18(n-19) = 0
n - 19 = 0 OR n - 18 = 0
Hence, n = 18 OR 19 ANS.
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I hope this helps!
____________________
a = 54 d = -3 and Sn = 513
So, Sn = n/2 [2a + (n-1) d ]
1026 = n [ 108 + (n-1) (-3) ]
1026 = n [ 108 -3n + 3]
1026 = n [ 111 -3n]
1026 = 111n - 3n²
3n² - 111n + 1026 = 0
n² - 37n + 342 = 0 {DIVISION BY 3}
On Splitting we have:
n² - 19n - 18n + 342 = 0
n(n-19) - 18(n-19) = 0
n - 19 = 0 OR n - 18 = 0
Hence, n = 18 OR 19 ANS.
____________________________
I hope this helps!
Thanx for the answer bro
Answered by
3
a=54
d= -3
Sn=513
n=?
Sn=n/2(2a+(n-1)d)
By substituting the values
513=n/2(2*54+(n-1)-3)
513=n/2(108-3n+3)
1026=111n-3n2
3n2-111n+1026=0
n2-37n+342=0
on solving this qudratic equation you will get
n=18,n=19
as both values of n are positive both are applicable
d= -3
Sn=513
n=?
Sn=n/2(2a+(n-1)d)
By substituting the values
513=n/2(2*54+(n-1)-3)
513=n/2(108-3n+3)
1026=111n-3n2
3n2-111n+1026=0
n2-37n+342=0
on solving this qudratic equation you will get
n=18,n=19
as both values of n are positive both are applicable
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