**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.**