Arithmetic Sequences
It consists in a series of terms with the condition that each term is calculated as the previous term plus a fixed number called the common difference (d).
The sequence is given as:
-30, -22, -14, -6,...
First, we need to find the common difference by subtracting two consecutive terms:
d = -22 - (-30) = -22 + 30 = 8
We can try another couple of terms:
d = -14 - (-22) = -14 + 22 = 8
If we test all the consecutive terms, we'll find the same value of d.
Now to use the formula:
an = a1 + (n - 1) * d
We need to find a1, the first term of the sequence. The value of a1 is -30.
Now we are ready to find the 20th term of the sequence (n=20) by substituting the values in the formula:
a20 = -30 + (20 - 1) * 8
Calculating:
a20 = -30 + 19 * 8 = -30 + 152 = 122
Thus the 20th term is 122