Given A.P is 7, 10, 13,…

Here, a₁ = a = 7, a₂ = 10

Common difference, d = a₂ – a₁ = 10 – 7 = 3

We know, a_n = a + (n – 1)d where a is first term or a₁ and d is common difference and n is any natural number

∴ a_n = 7 + (n – 1)3

⇒ a_n = 7 + 3n – 3

⇒ a_n = 3n + 4

To find total terms of the A.P., put a_n = 43 as 43 is last term of A.P.

∴ 3n + 4 = 43

⇒ 3n = 43 – 4

⇒ 3n = 39

⇒ n = 13

Hence, there are total 13 terms in the given A.P.