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# The Sum of First N Terms of an A.P. is 5n − N2. Find the Nth Term of this A.P. - Mathematics

Sum

The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.

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#### Solution

Let a be the first term and d be the common difference.
We know that, sum of first n terms = Sn =  $\frac{n}{2}$[2a + (n − 1)d] It is given that sum of the first n terms of an A.P. is 5n − n2.

∴ First term = =  S= 5(1) − (1)2 = 4.

Sum of first two terms = S= 5(2) − (2)2 = 6.

∴ Second term = S2 − S1 = 6 − 4 = 2.

∴ Common difference = d = Second term − First term
= 2 − 4 = −2

Also, nth term = an = a + (n − 1)d
⇒ an = 4 + (n − 1)(−2)
⇒ an = 4 − 2n + 2
⇒ an = 6 − 2n

Thus, nth term of this A.P. is 6 − 2n.

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 39 | Page 53
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