Question

. Find the middle term of the following AP:
a. 213, 205, 197, … … 37.
b. 7,13,19, … . .241

Answer 1

a= 213

d= a2-a1 = 205 - 213 = -8

now,

37= a+(n-1)d

37= 213 + (n-1)-8

37= 213 -8n +8

37= 221 -8n

8n=221 - 37

8n= 184

n=184/8

n=23

the middle most term would be 23/2 = 11.5 which is 12

an= a +(n-1)d

an= 213 +(12-1)-8

an= 213 -88

an=125

the middle term is 128