Question

Use the explicit formula an = a1 + (n - 1) • d to find the 350th term of the sequence below.

57, 66, 75, 84, 93, ...

A. 3234
B. 3207
C. 3141
D. 3198

Answer 1

that type has terms that increase linearly, the same amount each time 'd'

Answer 2

you know the start term, and the difference to the next 'd', that is all you need

Answer 3

hint:
the constant \(d\) of the series, is such that:
\[d = 93 - 84 = 84 - 75 = 75 - 66 = 66 - 57 = ...?\]

Answer 4

an = a1 + (n - 1) • d

n starts at 1, and results in a1, then every next term adds on an additional 'd' ,

any number term you want to know, it is just the first term value a1, and one less than the term number times the common difference 'd'

Answer 5

a1 + (n-1) d /. { a1 -> 57, n -> 350, d -> 66-57 }

/. means apply the replacement rules on the right to the expression on the left
and then evaluate the result.

What looks like mumbo jumbo on the right hand side is a list of replacement
rules from the Mathematica computer program. /. is the Mathematica replacement operator.

Did you get 3198 ?

Answer 6

Yes thanks @robtobey @DanJS