Question

Write a recursive formula for the following sequence: 3, 6, 12, 24, ....

an = an – 1 + 3; A1 = 3
an = an – 1 + 3n; A1 = 3
an = 2an – 1; A1 = 3
an = 3an – 1 – 3; A1 = 3
none of these

Answer 1

`\large\boxed{\left\{\begin{array}{ccc}a_1=3\\\\a_n=2a_(n-1)\end{array}\right}`

Explanation:

`a_1=3\\\\a_2=6=3\cdot2\to a_2=2a_1\\\\a_3=12=6\cdot2\to a_3=2a_2\\\\a_4=24=12\cdot2\to a_4=2a_3\\\vdots\\a_n=2a_(n-1)`