**5. Given the following sequence, determine whether it is arithmetic or not. If it is an Arithmetic Progression, find its general term : – 5, 2, 9, 16, 23, 30, ..... (3 marks)**

**Sol. – 5, 2, 9, 16, 23, 30, .....**

**t1 = – 5, t2 = 2, t3 = 9, t4 = 16, t5 = 23, t6 = 30**

**t2 – t1 = 2 – (– 5) = 2 + 5 = 7**

**t3 – t2 = 9 – 2 = 7**

**t4 – t3 = 16 – 9 = 7**

**t5 – t4 = 23 – 16 = 7**

**t6 – t5 = 30 – 23 = 7**

**Here, The difference between two consecutive terms is 7 which is a constant.**

**∴**

**The sequence is an A.P.**

**with a = t1 = – 5.**

**Common difference (d) = 7**

**tn = a + (n – 1) d**

**tn = – 5 + (n – 1) 7**

**tn = – 5 + 7n – 7**

**tn = 7n – 12**

**∴**

**The general term of A.P. is 7n – 12.**