Question

Write an explicit formula for the sequence {a_n}={-3,-1/2,2,9/2,7,...}. Then find a_17

Answer 1

A: a_n=5/2n-11/2;37

Explanation:

The guy above me is 100% correct. He gives the sequence, just plut 17 into n and then you will receive 37 as the answer. Please do not disregard his excellent work based on a disgruntled, ignorant individual which gave false ratings.

Answer 2

`a_n=\left\{-3,\ -(1)/(2),\ 2,\ (9)/(2),\ 7,\ ...\right\}\\\\a_1=-3\\\\a_2=-3+2(1)/(2)=-(1)/(2)\\\\a_3=-(1)/(2)+2(1)/(2)=2\\\\a_4=2+2(1)/(2)=4(1)/(2)=(9)/(2)\\\\a_5=4(1)/(2)+2(1)/(2)=7\\\\\text{The explicit formula of the nth term of the arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\d-common\ difference\\\\\text{We have}\ a_1=-3\ \text{and}\ d=2(1)/(2)=(5)/(2).\ \text{Substitute:}`

`a_n=-3+(n-1)\left((5)/(2)\right)=-(6)/(2)+(5)/(2)n-(5)/(2)=\boxed{(5)/(2)n-(11)/(2)=(5n-11)/(2)}`