Question

The sum of the first n terms of an AP is 5n-n^2. Find the nth term of this AP

Answer 1

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Answer 2

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