New Notes Blog: `2,8,14,20,...` Write an expression for the n'th term of the sequence. (There is more than one correct answer.)

Saturday, 21 December 2013

$\displaystyle{2},{8},{14},{20},\ldots$ Write an expression for the n'th term of the sequence. (There is more than one correct answer.)

Given the sequence: 2, 8, 14, 20, ...

The given sequence is an arithmetic sequence. The sequence is arithmetic because the common difference between each term is 6.

In this sequence the common difference is 6, therefore let d=6. The first term, $\displaystyle{a}_{{1}}$ is 2, therefore let $\displaystyle{a}_{{1}}={2}$ .

The formula to find the nth term of an arithmetic sequence is

$\displaystyle{a}_{{n}}={a}_{{1}}+{\left({n}-{1}\right)}{d}$

Substitute in the $\displaystyle{a}_{{1}}$ and d then simplify the expression.

$\displaystyle{a}_{{n}}={2}+{\left({n}-{1}\right)}{\left({6}\right)}$

$\displaystyle{a}_{{n}}={2}+{6}{n}-{6}$

$\displaystyle{a}_{{n}}={6}{n}-{4}$

...

Given the sequence: 2, 8, 14, 20, ...

The given sequence is an arithmetic sequence. The sequence is arithmetic because the common difference between each term is 6.

In this sequence the common difference is 6, therefore let d=6. The first term, $\displaystyle{a}_{{1}}$ is 2, therefore let $\displaystyle{a}_{{1}}={2}$ .

The formula to find the nth term of an arithmetic sequence is

$\displaystyle{a}_{{n}}={a}_{{1}}+{\left({n}-{1}\right)}{d}$

Substitute in the $\displaystyle{a}_{{1}}$ and d then simplify the expression.

$\displaystyle{a}_{{n}}={2}+{\left({n}-{1}\right)}{\left({6}\right)}$

$\displaystyle{a}_{{n}}={2}+{6}{n}-{6}$

$\displaystyle{a}_{{n}}={6}{n}-{4}$

Final Answer:

The expression for the nth term of the sequence is $\displaystyle{a}_{{n}}={6}{n}-{4}.$

New Notes Blog

Saturday, 21 December 2013

$\displaystyle{2},{8},{14},{20},\ldots$ Write an expression for the n'th term of the sequence. (There is more than one correct answer.)

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In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?

Saturday, 21 December 2013

Write an expression for the n'th term of the sequence. (There is more than one correct answer.)

No comments:

Post a Comment

In &quot;By the Waters of Babylon,&quot; under the leadership of John, what do you think the Hill People will do with their society?

$\displaystyle{2},{8},{14},{20},\ldots$ Write an expression for the n'th term of the sequence. (There is more than one correct answer.)

In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?