Question

Find the middle term of the AP. 95, 86, 77, ........, – 247.

Answer 1

Given A.P. is 95, 86, 77, ....., – 247

Here, a = 95, d = 86 – 95 = – 9

Let the A.P. has n terms.

Then, a_n = a + (n – 1)d

⇒ – 247 = 95 + (n – 1) (– 9)

⇒ – 247 = 95 – 9n + 9

⇒ – 247 = 104 – 9n

⇒ 9n = 104 + 247

⇒ 9n = 351

⇒ n = 39

Thus, the given A.P. has 39 terms.

Now, Middle term = `[1/2 (39 + 1)]^(th)` term

= `[1/2 (40)]^(th)` term

= 20^th term

a₂₀ = a + 19d

= 95 + 19 (– 9)

= 95 – 171

= – 76

As a result, the specified A.P.'s middle term is – 76.