if the sum of n terms …

It is given that sum of n terms of an A.P. is 3n² + 5n

=>  S₁ = 3(1)² + 5(1) = 3 + 5 = 8 which will also be 1st term as "a₁".

Further, S₂  = 3 (2)² + 5 (2) = 12 + 10 = 22

And, we know, a₂ = S₂ - S₁ = 22 - 8 = 14.... So, d = a₂ - a₁ = 14 - 8 = 6

Now, it's given that a_m = 164 => a₁ + (m - 1)d = 164

8 + (m - 1)$\times$6  = 164  => (m - 1)$\times$6 = 156 => (m - 1) = 26 => m = 27 (Answer)

According to question,

S₁ = a = 3(1)² + 5 x 1 = 8

S_{<font size="2">2</font>} = 3(2)^{<font size="2">2</font>} + 5 x 2 = 22                                Then,         a₂ = S₂ - S₁ = 22 - 8 = 14

S_{<font size="2">3</font>} = 3(3)^{<font size="2">2</font>} + 5 x 3 = 42                                Then,         a_{<font size="2">3</font>} = S_{<font size="2">3</font>} - S_{<font size="2">2</font>} = 42 - 22 = 22

Therefore, d = 14 - 8 = 6

Now, a_m = a + (m - 1)d = 164

=>          164 = 8 + (m - 1)6

=>          156 = (m - 1)6

=>          26 = m - 1

=>          m = 27