Obtain the sum of the 56 terms of an A. P. whose 19th and 38th terms are 52 and 148 respectively.

6. Obtain the sum of the 56 terms of an A. P. whose 19th and 38th terms are 52 and 148 respectively.

Sol. t19 = 52, t38 = 148

tn = a + (n – 1) d

∴  t19 = a + (19 – 1) d

∴  52 = a + 18d

∴  a + 18d= 52  ......(i)

t38 = a + (38 – 1) d

∴  148 = a + 37d

∴ a + 37d= 148 ......(ii)

Adding eq. (i) and (ii)

a + 18d + a + 37d = 52 + 148

∴ 2a + 55d = 200  ....... eq.(iii)

Sn = n/2[2a + (n – 1)d]

∴ S56 = 56/2[2a + (56 – 1) d]

∴ S56 = 28 [2a + 55d]

∴ S56 = 28 [200]   [From Eq. (iii)]

∴ S56 = 5600

∴ Sum of first 56 terms of A.P. is 5600.