# describe the nature of sequencewhat kind of sequence is that if the difference between 2 consecutive terms is always 2? what are the 6th and 7th terms?

nessus | High School Teacher | (Level 2) Adjunct Educator

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When I learned mathematics at school in England in around 1970 we were taught mathematical series, rather than sequences. The two words must mean the same thing. I would very much like to know if there is an international convention in maths like there is in chem or phys.

justaguide | College Teacher | (Level 2) Distinguished Educator

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A sequence where consecutive terms have a common difference is called an arithmetic sequence.

Here we know the common difference is 2.

The nth term of any arithmetic sequence is given by a + (n - 1)*d where a is the first term of the sequence and d is the common difference.

The 6th and 7th terms of the sequence that we need are given as a + 5d and a + 6d.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Since the difference between 2 consecutive terms is always 2, then the sequence is an arithmetic sequence.

To determine any term of an arithmetic sequence, we'll have to know 2 basic terms: the 1st term and the common difference. The common difference is 2 but the 1st term is not known.

Since the problem does not provide other constraint, we'll impose the following:

a2 + a3 = 8 (1)

By definition, the difference between 2 consecutive terms of an arithmetial progression is the common difference of the arithmetic sequence.

a3 - a2 = d

But, the common difference is d = 2, then:

a3 - a2 = 2 (2)

a2 + a3 + a3 - a2 = 8 + 2

We'll eliminate and combine like terms:

2a3 = 10

a3 = 10/2

a3 = 5

a2 = a3 - 2

a2 = 5 - 2

a2 = 3

But a2 = a1 + d

3 = a1 + 2

a1 = 3 - 2

a1 = 1

Since we know a1 and d, we'll determine a6 and a7:

a6 = a1 + 5d

a6 = 1 + 10

a6 = 11

a7 = 13