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

Question

Philoid · Accepted 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 = S₁ = 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 �_r = 5 + (r - 1)6 = 5 + 6r - 6 = 6r - 1

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

Find the rth term of the AP, the sum of whose first n terms is (3n2 + 2n).

Find the r^th term of the AP, the sum of whose first n terms is (3n² + 2n).