Question

What kind of sequence is the pattern 1, 6, 7, 13, 20, ...?

Answer 1

Answer:

The given sequence 6, 7, 13, 20, ... is a recursive sequence

Step-by-step explanation:

As the given sequence is

$6, 7, 13, 20, ...$

• It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.

As

$d = 7-6=1$,  $d = 13-7=6$

As d is not same. Hence, it cannot be an arithmetic sequence.

• It also cannot be a geometrical sequence and exponential sequence.

It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.

As

$r = 7-6=1$,  $r = 13-7=6$

$r = \frac{7}{6}$,  $r = \frac{13}{7}$

As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.

So, if we carefully observe, we can determine that:

• The given sequence 6, 7, 13, 20, ... is a recursive sequence.

Please have a close look that each term is being created by adding the preceding two terms.

For example, the sequence is generated by starting from 1.

     ${\displaystyle F_{1}=1$

and

     ${\displaystyle F_{n}=F_{n-1}+F_{n-2}}$

for n > 1.

Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence

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