Question

Find the middle term in the A.P 20, 16, 12, -----------

Answer 1

Solution:-

Given,

a = 20

d = 16-20 = 12-16

= -4

(1) If number of terms is odd

=> middle term=( n+1) /2 th term

=> a+[(n+1)/2-1]d

= 20+[(n-1)/2] (-4)

= 20-2n+2

= 22-2n

= 2(11-n)

(2) If number of terms is even

=> there are two middle terms

(i) n/2 th term

= a+(n/2-1)d

= 20+(n/2-1)×(-4)

= 20-2n+4

= 24-2n

= 2(12-n)

(ii) (n/2+1) th term

= a+[(n/2+1)-1]d

= 20+[n/2](-4)

= 20-2n

= 2(10-n)

hope this helps you