The sum of the first n terms of an A.P. is given by Sn = 2n2 + 5n , find the nth term of the A.P.
Sn =2n2 + 5n
Taking n = 1, we get
S1 = 2(1)2 + 5(1)
⇒ S1 = 2 + 5
⇒ S1 = 7
⇒ a1 = 7
Taking n = 2, we get
S2 = 2(2)2 + 5(2)
⇒ S2 = 8 + 10
⇒ S2 = 18
∴ a2 = S2 – S1 = 18 – 7 = 11
Taking n = 3, we get
S3 = 2(3)2 + 5(3)
⇒ S3 = 18 + 15
⇒ S3 = 33
∴ a3 = S3 – S2 = 33 – 18 = 15
So, a = 7,
d = a2 – a1 = 11 – 7 = 4
Now, we have to find the 15th term
an = a + (n – 1)d
an = 7 + (n – 1)4
an = 7 + 4n – 4
an = 3 + 4n
Hence, the nth term is 4n + 3.
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