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.
