Find the next four terms of the sequences: 2, 5, 8, 11 …

Solution:

Here, t1 = 2, t2 = 5, t3 = 8, t4 = 11

Here, t2 – t1 = 5 – 2 = 3

t3 – t2 = 8 – 5 = 3

t4 – t3 = 11 – 8 = 3

Therefore, we can see that the common difference between any two consecutive terms is 3

∴ We can get t5 , t6 , t7 and t8 by adding the common difference 3 to the preceding term.

∴ t5 = t4 + 3 = 11 + 3 = 14

∴ t6 = t5 + 3 = 14 + 3 = 17

∴ t7 = t6 + 3 = 17 + 3 = 20

∴ t8 = t7 + 3 = 20 + 3 = 23

Hence, the next four terms are 14, 17, 20 and 23 respectively.