Question

For the sequence 3, 8, 13, 18, 23, ….: (i) Find recursive and non-recursive formulas. (ii) Prove the non-recursive formula using recursive formula and by induction. (iii) Write and iterative algorithm to out put the first m terms.

Answer 1

Explanation:

Given is the sequence 3, 8, 13, 18, 23, ….:

We find that this is a geometric sequence with each term added with 5 to the previous term

Hence recursive formula is
`a_n =a_(n-1) +5`

Non recursive formula:

`a_n =a_(n-1) +5=a_(n-2) +2(5)\\=a_(n-3) +3(5)-...\\=a_(n-(n-1)) +5(n-1)\\=a_1+(n-1)5\\=3+5n-5\\=5n-2`

iii) Start with 3.

Add 5 and write as 2nd term

Take the resulting term and add 5 and mark as 3rd term

Repeat this m times.