If S_n = 2n² + 3n, then d =_____

We have S_n = 2n² + 3n from the question.

We know that, S_n = × (2a + (n – 1)d)

So we can say that,

⇒ 2n² + 3n = × (2a + (n – 1)d)

⇒ 4n² + 6n = n × (2a + (n – 1)d)

⇒ 4n² + 6n = 2na + dn² – dn

⇒ 4n² + 6n = dn² + (2a – d)n

Now comparing the coefficients of “n^2” and “n”, we get that,

d = 4

∴ the correct option is (b).