Question

An AP consist of 21 terms the sum of three middle terms is 63 and sum of last three term is 90. Find the AP

Answer 1

The three middle terms are T10, T11 and T12

T10 + T11 +T12 = 63

=> a+9d +a+10d +a+11d = 63

=> 3a+30d = 63

=> a+10d = 21 --------(1)

Last Three terms are T19,T20 and T21

T19 + T20 + T21 = 90

=> a+18d +a+19d + a+20d = 90

=> 3a + 57d = 90

=> a+19d = 30 -------(2)

On subtracting equation 1 from 2, we get

9d = 9

=> d = 1

Now,

On putting the value of d in equation 1, we get

a+10* 1 = 21

=> a+10 = 21

=> a = 11


Required AP is 11, 12, 13, .......... Upto 21 terms