Question

Find the middle term of the AP 213, 205, 197, .............., 37.​

Answer 1

Step-by-step explanation:

nth term is 23

middle term of the ap is (n+1)/ 2

24/2=12

12th term is the middle term of the ap

a12 =213 + 12 *(-8)=125

Answer 2

Answer:

Here a = 213 and d= 205-213= -8 .

Let the given AP contain n terms . Then ,

Tn =37

=> a + (n-1)d =37

=> 213 + (n- 1) × -8 = 37

=> 221 - 8n =37

=> 8n =221- 37 =184

=> n = 23 .

Thus , the given AP contains 23 terms .

Therefore , it's midle term

= 1/2 ( 23 +1) th term

= 12 th term

So , middle term = T12 = (a+11d )

=213 + 11× -8

= 213 -88 = 125 .

Hence, the middle term is 125 .

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