Find the recursive formula for the nth term of the sequence given below. 2, 14, 34, 62, 98, ...

Frances Simon
2022-04-09
Answered

This subject is called Discrete mathematics.

Find the recursive formula for the nth term of the sequence given below. 2, 14, 34, 62, 98, ...

Find the recursive formula for the nth term of the sequence given below. 2, 14, 34, 62, 98, ...

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entreblogsmc2j

Answered 2022-04-10
Author has **10** answers

Definition:

Recursive formulae in a sequence:

It is a formulae to find the next term in sequence using one or more previous terms which are given.

In an arithmetic sequence, recursive formulae is given as:

${a}_{n}+1=an+d$

Where d is common difference.

The given sequence is:

2,14,34,62,98......

Find the first difference:

12, 20, 28, 36, 44.....

Find the second difference:

8,8,8,8......

Here, second difference of the given sequence is same.

Find general term of terms of first difference 12, 20, 28, 36, 44....., since, it is an arithmetic sequence.

Therefore, general term is:$12+(n-1)8=4+8n$

Recursive formulae for given sequence is:

${a}_{n}+1={a}_{n}+4+8n$

Answer:

${a}_{n}+1={a}_{n}+4+8n$

Recursive formulae in a sequence:

It is a formulae to find the next term in sequence using one or more previous terms which are given.

In an arithmetic sequence, recursive formulae is given as:

Where d is common difference.

The given sequence is:

2,14,34,62,98......

Find the first difference:

12, 20, 28, 36, 44.....

Find the second difference:

8,8,8,8......

Here, second difference of the given sequence is same.

Find general term of terms of first difference 12, 20, 28, 36, 44....., since, it is an arithmetic sequence.

Therefore, general term is:

Recursive formulae for given sequence is:

Answer:

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