Question

Find the middle term of the A.P. 213, 205, 197, … 37?​

Answer 1

Answer:

According to the question:-

First term (a) = 213

Common d difference (d)

= 205 - 213

= -8

Also,

l = 37 , also number of term = n

Using formula we have,

= a + (n - 1)d

37 = 213 + (n - 1) (- 8)

37 - 231 = -8(n - 1)

n - 1 = -176/-8

n = 22 + 1

n = 23

Now,

Middle term

= 23 + 1/2

= 12th

So,

a(12) = a + (n - 1)d

a(12) = 213 + (12 - 1)(-8)

a(12) = 213 - 88

a(12) = 125

Therefore,

Middle term = 125

Step-by-step explanation:

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Answer 2

☆ ANSWER ☆:-

Let a= first term of A.P., d=common difference

nth term, an=a+(n−1)d;

Here a=213, d=205−213=−8, an=37

an=a+(n−1)d

⇒37=213+(n−1)(−8)

⇒176=8(n−1)

⇒8n=184

⇒n=23

⇒ Middle term =23+1/2=12th term

⇒a12 = a+11d = 213−88 = 125.

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