(i) The nth term of a sequence S is n3 + 2. Write down the first 4 terms of the sequence
(ii) The first four terms of another sequence T are 4, 12, 32 and 70
By comparing S & T, find the 5th term of T
(iii) Find, in terms of n, an expression for the nth term of sequence T
Answer:
(i)
1st term --------- 13 + 2 = 3
2nd term----------23 + 2 = 10
3rd term-----------33 + 2 = 29
4th term------------43 + 2 = 66
Thus, the number sequence is 3, 10, 29, 66
(ii)
Compare:
1. 3, 10, 29, 66 ---- S
2. 4, 12, 32, 70 ----- T
1st term of T is S + 1
2nd term of T is S + 2
3rd term of T is S + 3
4th term of T is S + 4
5th term= 53 + 2 +5 = 132
(iii) nth term of T is S + n
Thus, nth term of T = n3 + n + 2
