If the sum of the first …
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Gaurav Seth 4 years, 10 months ago
We have given that
Sum of the first n terms = 4n – n2
⇒ Sn = 4n – n2
Put, n = 1, then
S1 = 4(1) – (1)2 = 4 – 1 = 3
⇒ d1 = 3
Hence, the first term is
Put n = 2, then
S2 = 4(2) – (2)2
= 8 – 4 = 4
Hence, the sum of two terms is 4.
Now, second term = S2 – S1 = 4 – 3 = 1
Put n = 3, then
S3 = 4(3) – (3)2
= 12 – 9 = 3
Third term = S3 – S2 = 3 – 4 = –1
Put n = 9, 10
S9= 4(9) – (9)2
= 36 – 81 = –45
S10= 4(10) – (10)2
= 40 –100 = –60
∴ Tenth term = S10 – S9
= – 60 – (–45)
= – 60 + 45 = –15
Now, Sn –1 = 4(n – 1) – (n – 1)2
= (4n – 4) – (n2 + 1 – 2n)
= 4n – 4 – n2 – 1 + 2n
= 6n – n2 – 5
∴ nth term = Sn – Sn – 1
= (4n – n2) – (6n – n2 – 5)
= 4n – n2 – 6n + n2 + 5
= 5 –2n
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