Q. 113.8( 4 Votes )

# Find the r^{th} term of the AP, the sum of whose first n terms is (3n^{2} + 2n).

Answer :

Given: The sum of first n terms.

To Find: The r^{th} term.

Let the first term be a and common difference be d

Put n = 1 to get the first term

a = S_{1} = 3 + 2 = 5

Put n = 2 to get a + (a + d)

2a + d = 12 + 4 = 16

10 + d = 16

d = 6

t_{r} = a + (r - 1)d

t ï¿½_{r} = 5 + (r - 1)6 = 5 + 6r - 6 = 6r - 1

The r^{th} term is given by 6r - 1.

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