Answer:
C. \(a_3_0=-101\)
Step-by-step explanation:
We have the arithmetic sequence 15,11,7,3,-1,...
Where,
\(a_1=15,\\a_2=11,\\a_3=7,\\a_4=3,\\a_5=-1,...\)
You can see that the common difference d=(-4), or if you couldn't see the common difference you can calculate it with the formula:
\(d=a_n_+_1-a_n\)
Then,
\(d=a_2-a_1\\d=11-15\\d=(-4)\)
Now to find the 30th term of the arithmetic sequence we can use the following formula:
\(a_n=a_1+(n-1).d\)
Replacing n=30, \(a_1=15\) and d=(-4):
\(a_n=a_1+(n-1).d\\a_3_0=15+(30-1)(-4)\\a_3_0=15-29.4\\a_3_0=15-116\\a_3_0=-101\)
Then the correct option is C. \(a_3_0=-101\)
