Q. 3 A4.7( 9 Votes )

# 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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