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lara [203]
3 years ago
10

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.
Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
7 0

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.

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