Question

Find the middle term of the ap 213 205................137

Answer 1

Answer is 171
We know that
Middle term=a+c/2
205+137/2=171

Answer 2

Answer:

The middle term is 173.

Step-by-step explanation:

Given : A.P 213,205,.....137

To find : Find the middle term of the AP?

Solution :

A.P - 213,205,.....137

Where, first term a=213

Common difference is d=10-6=-8

Last term is $a_n=137$

The formula of nth term is $a_n=a+(n-1)d$

Substitute the values in the formula,

$137=213+(n-1)-8$

$137-213=-8n+8$

$-76-8=-8n$

$-84=-8n$

$n=\frac{84}{8}$

$n=10.5$

Number of terms are 11.

The middle term is the 6th term.

So, $a_n=a+(n-1)d$

$a_6=213+(6-1)-8$

$a_6=213+(5)-8$

$a_6=213-40$

$a_6=173$

So, The middle term is 173.