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.

#### Question

#### 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.