Which of the following are possible explicit formulas for the nth term of the constant velocity sequence below? Check all that apply. 10, 17, 24, 31, ...

We have an arithmetic progression:

Nth=an

an=a₁ + (n-1) d

a₁ is the first term.

n=number of terms.

d=common difference

10,17,24,31 ...

a₁=10

d=a₂-a₁=17-10=7

Therefore:

Nth=an

an=a₁ + (n-1) d

an=10 + (n-1) 7

an=10+7n-7

an=7n+3.

Therefore: the formula for the nth is, an=a + (n-1), in this case; an=7n+3,

To check:

a₁=7*1+3=10

a₂=7*2+3=17

a₃=7*3+3=24

a₄=7*4+3=31

a₅=7*5+3=38 ...