Mathematics
In an A.P., the sum of its first n terms is 6n - n2. Find its 25th term.
AP GP
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Answer
Given, Sn = 6n - n2.
So, sum of (n -1) terms will be
⇒ Sn - 1 = 6(n - 1) - (n - 1)2
⇒ Sn - 1 = 6n - 6 -(n2 + 1 - 2n)
⇒ Sn - 1 = 6n - 6 - n2 - 1 + 2n
⇒ Sn - 1 = 8n - n2 - 7.
By formula, an = Sn - Sn - 1
⇒ an = 6n - n2 - (8n - n2 - 7)
⇒ an = 6n - 8n - n2 + n2 + 7
⇒ an = -2n + 7.
∴ a25 = -2(25) + 7 = -50 + 7 = -43.
Hence, the 25th term of the A.P. is -43.
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