Question

Find middle term in AP-1,5,9,13------169

Answer 1

Hey there !

Solution:

AP : 1, 5, 9, 13

In this AP,

First Term ( a ) = 1

Common Difference ( d ) = + 4

Number of terms ( n ) = ?

Final Term ( $a_n$ ) = 169

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

Substituting all the values in the formula we get,

=> 169 = 1 + ( n - 1 ) 4

=> 169 - 1 = ( n - 1 ) 4

=> 168 = ( n - 1 ) 4

=> n - 1 = 168 / 4

=> n - 1 = 42

=> n = 43.

So the number of terms in the AP is 43.

Since the number of terms is odd, the formula for calculating the middle term is :

Middle term of an odd number = $\frac{n + 1 }{2}$

Where 'n' represents the number of terms.

So the Middle term in this case would be : $\frac{43 + 1 }{2} = \frac{44}{2} = 22$

Hence the middle most term is 22nd term.

The value of 22nd term is : $a_{22} = a + 21 d$

$a_{22} = 1 + 21 ( 4 ) \\ a_{22} = 1 + 84 \\ a_{22} = 85$

So the middle most term is 85.

Hope my answer helped !