Question

How many terms are in the arithmetic sequence shown below?15, 7, -1, -9...,-225

Answer 1

We know that

We can write an Arithmetic Sequence as a rule:

an = a1 + d(n−1)

where

a1 = the first term
d =the "common difference" between terms

in this problem
a1=15  a2=7  a3=-1  a4=-9  .....    an=-225
d=a2-a1  
d=7-15-----> d=-8

an = a1 + d(n−1)
for
an=-225
d=-8
a1=15
find n
-225=15+(-8)*(n-1)--> (n-1)=[-225-15]/-8----> n-1=30---> n=30+1---> n=31

the answer is
31