## anonymous one year ago What types of functions combine to create an explicit formula for arithmetic sequences?

1. freckles

what does your question mean ?

2. freckles

$a,a+d,a+2d,a+3d,... ,a+(n-1)d,... \text{ where the } nth \text{ term is given by } \\ a_n=a+(n-1)d$

3. freckles

by the way the above is an arithemetic sequence because the common difference is d

4. freckles

that is term - previous term will always give you d

5. anonymous

functions that allow the calculation of any term in the sequence ??|

6. freckles

you can use the above formula to find a term a_k if you know d and the first term

7. freckles

for example say your first term is 5 and your common difference is 3 and you want to find a_(55) $a_n=5+(n-1)3 \\ \text{ well } a_{55}=5+(55-1)3=5+(54)3=5+162=167$