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 a_n

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