Question

Find the middle term of the AP 6,13,20,....,216.

Answer 1

AP = 6 , 13 , 20 , .............., 216


Here,


First term ( a ) = 6


Common difference ( d ) = 13 - 6 = 7



Last term ( Tn ) = 216



Tn = 216



a + ( n-1) × d = 216


6 + ( n - 1 ) × 7 = 216


6 + 7n - 7 = 216



7n - 1= 216


7n = 216 + 1


n = 217/7

n = 31


Number of terms = 31.


Thus , the given AP contains 31 terms.



Therefore ,


It's middle term = 1/2 × (31+1) = 16th term.

So, the middle term = T16 = ( a + 15d )

=> 6 + 15 × 7


=> 6 + 105

=> 111