ARITHMETIC SEQUENCE
an = a1 + (n-1)d
.
The formula above is used to get the nth term of an arithmetic sequence, but we can also use it to know the number of terms (n).
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Given:
a1 = 4
d = a2 - a1 = 1 - 4 = -3
an = -29
n = ?
.
Solution:
an = a1 + (n-1)d
-29 = 4 + (n-1)-3
-29 = 4 + (-3n + 3)
-29 = -3n + 7
-29 - 7 = -3n
-36 = -3n
-36/-3 = -3n/-3
12 = n
.
Therefore, -29 is the 12th term of the arithmetic sequence 4, 1, -2, -5, ...
