Question

Find the 95th term of the arithmetic sequence 4, -5, -14,...
Answer:

Answer 1

Answer: a₉₅=-842

Explanation:

The arithmetic sequence 4, -5, -14,...

`a_n=a_1+(n-1)d\\\\d=a_2-a_1\\\\d=-5-4\\\\d=-9\\\\a_(95)=4+(95-1)(-9)\\\\a_(95)=4+94(-9)\\\\a_(95)=4-846\\\\a_(95)=-842`

Answer 2

Each term is subtracted by 9.
The first term is 4
f(n) = 4 - 9n
f(0) = 4 - 9(0) First term
f(1) = 4 - 9(1) = -5 Second term
f(2) = 4 - 9(2) = -4 Third term
f(94) = 4 - 9(94) = -842

The 95th term is -842. (I substitute in a number one less as that is how the pattern seems to work, there is probably a better way to do it but that is the right answer. Hope this helps.