Question

Find the formula for the nth term in the given sequence 12,36,108,324,972​

Answer 1

`\huge\boxed{a_n=12\cdot3^(n-1)=4\cdot3^n}`

Explanation:

`a_1=12\\\\a_2=36=3\cdot12=3a_1\\\\a_3=108=3\cdot36=3a_2=3\cdot3a_1=3^2a_1\\\\a_4=324=3\cdot108=3a_3=3\cdot3^2a_1=3^3a_1\\\\a_5=972=3\cdot342=3a_4=3\cdot3^3a_1=3^4a_1\\\vdots\\a_n=3^(n-1)a_1=3^(n-1)\cdot12\\\\3^(n-1)\cdot12=3^(n-1)\cdot3\cdot4=3^(n-1+1)\cdot4=4\cdot3^n`

`\text{Used}\\\\a^n\cdot a^m=a^(n+m)`