Verified answer

Answer:

17,21

Step-by-step explanation:

Given Series is -15, -11, ... 53.

First term = a = -15.

Common difference d = -11 + 15 = 4.

Let us assume that there are n terms in the given A.P. then,

an = 53.

⇒ -15 + (n - 1) * 4 = 53

⇒ -15 + 4n - 4 = 53

⇒ -19 + 4n = 53

⇒ 4n = 72

⇒ n = 18

Thus, the given AP consists of 18 terms.

Since the number of terms is even, there will be two middle terms.

Middle term of the given A.P:

(i) 1st term:

= (n/2) th term

= 9th term

= a + (9 - 1) * d

= a + 8d

= -15 + 8(4)

= -15 + 32

= 17.

(ii) 2nd term:

= (n/2 + 1)th term

= 10th term

= a + 9d

= -15 + 9(4)

= -15 + 36

= 21.

Therefore, the middle terms are 17 and 21.

Hope it helps!