Question

Find the pattern and use it to list the nth term in the sequence.

1, 1/32,1/243,1/1024,1/3125

Answer 1

`1;\ (1)/(32);\ (1)/(243);\ (1)/(1024);\ (1)/(3125)\\\\1=(1)/(1^5)\\\\(1)/(32)=(1)/(2^5)\\\\(1)/(243)=(1)/(3^5)\\\\(1)/(1024)=(1)/(4^5)\\\\(1)/(3125)=(1)/(5^5)\\\vdots\\\\a_n=(1)/(n^5)\ where\ n\in\mathbb{N^+}`