Given, 

a_n = 2n + 7 

We can find first five terms of this sequence by putting values of n from 1 to 5. 

When n = 1 : 

a₁ = 2(1) + 7 

⇒ a₁ = 2 + 7 

⇒ a₁ = 9 

When n = 2 : 

a₂ = 2(2) + 7 

⇒ a₂ = 4 + 7 

⇒ a₂ = 11 

When n = 3 : 

a₃ = 2(3) + 7 

⇒ a₃ = 6 + 7 

⇒ a₃ = 13 

When n = 4 : 

a₄ = 2(4) + 7 

⇒ a₄ = 8 + 7 

⇒ a₄ = 15 

When n = 5 : 

a₅ = 2(5) + 7 

⇒ a₅ = 10 + 7 

⇒ a₅ = 17 

∴ First five terms of the sequence are 9, 11, 13, 15, 17. 

A.P is known for Arithmetic Progression whose common difference 

= a_n – a_n-1 

Where n > 0 

a₁ = 9, a₂ = 11, a₃ = 13, a₄ = 15, a₅ = 17 

Now,

a₂ – a₁ = 11 – 9 = 2 

a₃ – a₂ = 13 – 11 = 2 

a₄ – a₃ = 15 – 13 = 2 

a₅ – a₄ = 17 – 15 = 2 

As, 

a₂ – a₁ = a₃ – a₂ = a₄ – a₃ = a₅ – a₄ 

The given sequence is A.P 

Common difference, 

d = a₂ – a₁ = 2 

To find the seventh term of A.P, firstly find an 

We know,

a_n = a + (n-1)d 

Where a is first term or a₁ and d is common difference 

∴ a_n = 3 + (n-1) 2 

⇒ a_n = 3 + 2n – 2 

⇒ a_n = 2n + 1 

When n = 7 : 

a₇ = 2(7) + 1 

⇒ a₇ = 14 + 1 

⇒ a₇ = 15 

Hence, 

The 7^th term of A.P. is 15