**8. The 11th term and the 21st term of an A.P. are 16 and 29 respectively, find :**

**(i) the 1st term and the common difference.**

**(ii) the 34th term**

**(iii) ‘n’ such that tn = 55.**

**Sol. tn = a + (n – 1) d**

**∴**

**t11 = a + (11 – 1) d**

**16 = a + 10d**

**∴**

**a + 10d = 16**

**∴**

**a = 16 – 10d .......(i)**

**∴**

**t21 = a + (21 – 1) d**

**29 = a + 20d**

**∴**

**a + 20d = 29 ......(ii)**

**Substituting eq. (i) in eq. (ii)**

**∴**

**a + 20d = 29 ......(ii)**

**∴**

**16 – 10d + 20d = 29**

**∴**

**10d = 29 – 16**

**∴**

**10d = 13**

**∴**

**d =**

^{13}/_{10}**∴**

**d = 1.3**

**Substituting d = 1.3 in eq. (i)**

**a = 16 – 10d .......(i)**

**∴**

**a = 16 – 10 (1.3)**

**∴**

**a = 16 – 13**

**∴**

**a = 3**

**The first term is 3 and the common difference is 1.3**

**(ii) the 34th term**

**Sol. tn = a + (n – 1) d**

**t34 = a + (34 – 1) d**

**∴**

**t34 = 3 + 33 (1.3)**

**∴**

**t34= 3 + 42.9**

**∴**

**t34 = 45.9**

**∴**

**Thirty fourth term of A.P. is 45.9.**

**(iii) ‘n’ such that tn = 55. (1 mark)**

**Sol. tn = a + (n – 1) d**

**∴**

**55 = 3 + (n – 1) d**

**∴**

**55 = 3 + (n – 1) 1.3**

**∴**

**55 = 3 + 1.3n – 1.3**

**∴**

**55 = 1.7 + 1.3n**

**∴**

**53.3 = 1.3n**

**∴**

**n =**

^{53.3}/_{1.3}**∴**

**n =**

^{53.3}/_{1.3}×^{10}/_{10}**∴**

**n =**

^{533}/_{13}**∴**

**n = 41**