Question
It is given that 38, 35, 32,... is an arithmetic sequence. Mandy claims that there are 14 positive terms in the sequence. Do you agree? Explain your answer.
Answer
Since the sequence 38, 35, 32, … is an arithmetic sequence, it is obvious from the given terms that the 1st term a_1=38, the common difference d=-3.
Apply the formula for the general terms of an arithmetic sequence
a_n=a_1+(n-1)d
If a_n>0
a_1+(n-1)d>0
38+(n-1)(-3)>0
-3n+3 >-38
3n<41
n<13\dfrac{2}{3}
Therefore, what Mandy claims is not correct. There are 13 positive terms.