Question

Write an expression to represent the pattern.
19, 27, 35, 43...

Answer 1

Answer:
`\Huge\boxed{a_n=19+8(n-1)}`

Explanation:

Given sequence

`19,~27,~35,~43~...`

Given arithmetic sequence expression

`a_n=a_1+d(n-1)`

`a_n=nth~term`

`a_1=1^(st)~term`

`\text{d=Common~{difference}}`

`n=nth~position`

Determine the common difference

`27-19=\underline{8}`

`35-27=\underline{8}`

`43-35=\underline{8}`

`d=\large\boxed{8}`

Substitute values into the given expression

`a_n=(19)+(8)(n-1)`

`\Huge\boxed{a_n=19+8(n-1)}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

Explanation:

This represents an arithmetic sequence, modeled by the formula

`a_n=a_1+d(n-1)` where a1 is the first term, d is the common difference, and n stands for the position in the sequence. For example, the number 27 is in the second position, so a2 = 27. We need to find the common difference, the same number either added in or subtracted away that will get us from one number to the next. To get from a1 = 19 to a2 = 27, we add 8. Then to get from 27 to 35 we add 8. Likewise, for the difference between 43 and 35. So d = 8. Our formula is

`a_n=19+8(n-1)` and simplify a bit to

`a_n=19+8n-8` and a bit more to

`a_n=8n+11`

As you can see, arithmetic sequence formulas always represent straight lines!