Find the number of terms in the aritmetic progession 2,-9,-20,-141

2 answers

the common difference is -11 , so there appear to be 10 terms "missing" between -20 and -141
a = 2, d = -11

term(n) = a + (n-1)d
-141 = 2 + (n-1)(-11)
-143 = -11n + 11
11n = 154
n = 14
there are 14 terms in the sequence.

(check by listing them, there are not that many)