Question

Find a formula for the nth term of the sequence in terms of n. one ninth comma two twelfths comma StartFraction 2 squared Over 15 EndFraction comma StartFraction 2 cubed Over 18 EndFraction comma StartFraction 2 Superscript 4 Over 21 EndFraction comma ... 1 9 , 2 12 , 22 15 , 23 18 , 24 21 , ... a Subscript n an equals = nothing for n greater than or equals 1 n≥1

Answer 1

`a_n=(2^(n-1))/(9+3(n-1)), n\geq 1`

Explanation:

The sequence is given as:

`(1)/(9), (2)/(12),(2^2)/(15),(2^3)/(18), (2^4)/(21) \cdots`

The numerator is a power of n with the starting term being
`2^0`

The denominator is being increased by 3 with the starting term being 9.

Therefore, the nth term of the sequence is:

`a_n=(2^(n-1))/(9+3(n-1)), n\geq 1`