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

Answer:

Step-by-step 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.