Find:

10^th term of the A.P. 1, 4, 7,10,.....

A.P is known for Arithmetic Progression whose common difference = a_n – a_n-1 where n > 0

a = a₁ = 1, a₂ = 4

Common difference, d = a₂ – a₁ = 4 – 1 = 3

To find the tenth term of A.P, firstly find a_n

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

∴ a_n = 1 + (n-1) 3

⇒ a_n = 1 + 3n – 3

⇒ a_n = 3n – 2

When n = 10:

a₁₀ = 3(10) – 2

⇒ a₁₀ = 30 – 2

⇒ a₁₀ = 28

Hence, 10^th term of A.P. is 28