What is the 40th term of the arithmetic sequence?
21,18,15,12,9....
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
The 40th term of the arithmetic sequence 21,18,15,12,9.. is -96
using Arithmetic progression formula,
a = first term = 21
common difference = d = 18 - 21 = - 3
Therefore,
aₙ = a + (n - 1)d
a₄₀ = 21 + (40 - 1)-3
a₄₀ = 21 +(39)(-3)
a₄₀ = 21 - 117
a₄₀ = -96
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