Question

Find the middle term of the A.P. 213, 205, 197, ---, 37.

Answer 1

Here,

a = 213

d = 205−213 = −8

Let the number of terms in the given AP be n.

We know

a_n=a+(n−1)d

⇒37=213+(n−1)(−8)

⇒8(n−1)=176

⇒n−1=22

⇒n=23

Thus, there are 23 terms in the given AP.

So, the (`(23+1)/2`)th term, i.e. the 12th term, will be the middle term.

∴ a₁₂=213+(12−1)(−8)

⇒a₁₂=213−88

⇒a₁₂=125

Thus, 125 is the middle term of the given AP