Given the following sequence, determine if it is arithmetic or not. If it is an Arithmetic Progression, find its general term. 5, 2, – 2, – 6, – 11, .....

6. Given the following sequence, determine if it is arithmetic or not. If it is an Arithmetic Progression, find its general term. 5, 2, – 2, – 6, – 11, .....

Sol. 5, 2, – 2, – 6, – 11, .....

t1 = 5, t2 = 2, t3 = – 2, t4 = – 6, t5 = – 11

t2 – t1 = 2 – 5 = – 3

t3 – t2 = – 2 – 2 = – 4

t4 – t3 = – 6 – (– 2) = – 6 + 2 = – 4

t5 – t4 = – 11 – (– 6) = – 11 + 6 = – 5

Here, The difference between two consecutive terms is not a constant.

∴  The sequence is not an A.P.

– 10, – 13, – 16, – 19, .....

(viii) – 10, – 13, – 16, – 19, ..... (1 mark)

Sol. t1 = – 10, t2 = – 13, t3 = – 16, t4 = – 19

t2 – t1 = – 13 – (– 10) = – 13 + 10 = – 3

t3 – t2 = – 16 – (– 13) = – 16 + 13 = – 3

t4 – t3 = – 19 – (– 16) = – 19 + 16 = – 3

 Here, The difference between ANY two consecutive terms is – 3 which is constant.

∴  The sequence is an A.P.