Question

Find the explicit formula that produces the given sequence.
3/2, 3/4, 3/8, 3/16,...

Answer 1

`(3)/(2);\ (3)/(4);\ (3)/(8);\ (3)/(16);\ ...\\\\a_1=(3)/(2)\\\\a_2=(3)/(4)=(3)/(2)\cdot(1)/(2)\\\\a_3=(3)/(8)=(3)/(4)\cdot(1)/(2)=(3)/(2)\cdot\left((1)/(2)\right)^2\\\\a_4=(3)/(16)=(3)/(8)\cdot(1)/(2)=(3)/(2)\cdot\left((1)/(2)\right)^3\\\vdots`

`a_n=(3)/(2)\cdot\left((1)/(2)\right)^(n-1)=(3)/(2)\cdot\left((1)/(2)\right)^(-1)\cdot\left((1)/(2)\right)^n=(3)/(2)\cdot2\cdot\left((1)/(2)\right)^n=3\cdot\left((1)/(2)\right)^n`