Question

find the middle term of AP and AP is 6,13,20,.........,216

Answer 1

Is it right or wrong if wrong te the correct one

Answer 2

Answer:

• Middle term of A.P. is 111.

Step-by-step explanation:

Given:

AP = 6, 13, 20,........, 216

To Find:

Middle term of A.P.

Now, we know that first term of A.P. is a₁.

⇒ a₁ = 6

And, 2nd term of A.P is a₂,

⇒ a₂ = 13

Common difference, d = a₂ - a₁

⇒ d = 13 - 6

⇒ d = 7

Now, first we will calculate total number of terms,

⇒ Tₙ = a + (n - 1)d

⇒ 216 = 6 + (n - 1)7

⇒ 216 = 6 + 7n - 7

⇒ 216 = 7n - 1

⇒ 216 + 1 = 7n

⇒ 217 = 7n

⇒ n = 217/7

⇒ n = 31th term.

Now, we will find middle term,

⇒ Middle term = (31 + 1)/2

⇒ Middle term = 16th term.

Now, we will calculate 16th term,

⇒ aₙ = a + (n - 1)d

⇒ a₁₆ = 6 + (16 - 1)7

⇒ a₁₆ = 6 + (15)7

⇒ a₁₆ = 6 + 105

⇒ a₁₆ = 111

Hence, Middle term of A.P. is 111.