What is the 40th term of the arithmetic sequence?

21,18,15,12,

a: -99
b: -96
c: 6
d: 138

We start off with 21 as the first term. So a1 = 21

The common difference is d = -3 because we subtract 3 each time to get from one term to the other (eg: 21 to 18 is minus 3)

The nth term of an arithmetic sequence is found by using this formula

an = a1 + d(n-1)

let's plug in the values we have so far to get

an = 21 + (-3)(n-1)
an = 21 - 3(n-1)
an = 21-3n+3
an = -3n+24

Why do this? Well it's helpful so we can find any term in the formula we want. In this case, we want the 40th term. So just plug in n = 40 from here and you're done

an = -3n+24
a40 = -3*40+24
a40 = -96

pointing you to the answer of choice B) -96

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