The sum of the first n terms of an AP is 5n-n^2. Find the nth term of this AP
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Answered by
11
Hey.. I think this can be ur answer!!
Hope it helps you dear ☺️☺️
Hope it helps you dear ☺️☺️
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Hasti152002:
hmm
ya i got it
what is it?
you took the common diff and the 2nd term as same
that is incorrect
oh ha
yaa
did you get it ??
done got it!! thx
alright no problem
Answered by
21
Sⁿ = n/2 * ( 2a + [ n - 1 ] d )
Now,
here
Sⁿ = 5n - n²
∴ By substituting n-1 in place of the n
We get,
Sⁿ⁻¹ = 5(n-1) - ( n - 1 )²
= 5n - 5 - ( n² + 1 - 2n )
= 5n - 5 - n² - 1 + 2n
= -n² + 7n - 6
∴Sⁿ⁻¹ = -n² + 7n - 6
Now,
we know that
termⁿ = Sⁿ - Sⁿ⁻¹
By substituting the values here, for Sⁿ & Sⁿ⁻¹ we will get the value for termⁿ.
Termⁿ = 5n - n² - ( -n² + 7n - 6 )
Termⁿ = 5n - n² + n² - 7n + 6
Termⁿ = 6 - 2n
∴ The nth term of the given A.P is 6 - 2n.
Hope this helps you !!
# Dhruvsh
Now,
here
Sⁿ = 5n - n²
∴ By substituting n-1 in place of the n
We get,
Sⁿ⁻¹ = 5(n-1) - ( n - 1 )²
= 5n - 5 - ( n² + 1 - 2n )
= 5n - 5 - n² - 1 + 2n
= -n² + 7n - 6
∴Sⁿ⁻¹ = -n² + 7n - 6
Now,
we know that
termⁿ = Sⁿ - Sⁿ⁻¹
By substituting the values here, for Sⁿ & Sⁿ⁻¹ we will get the value for termⁿ.
Termⁿ = 5n - n² - ( -n² + 7n - 6 )
Termⁿ = 5n - n² + n² - 7n + 6
Termⁿ = 6 - 2n
∴ The nth term of the given A.P is 6 - 2n.
Hope this helps you !!
# Dhruvsh
nice answer bhai
thank you so much di !!!
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