In a Go kp^3,k^2p^5,k^3p^7,.... Find the 9th term. The nth term and simplify your result. What does the result becomes if KP=10
The given sequence is: kp^3, k^2p^5, k^3p^7, ...
To find the nth term, we first notice a pattern that the power of p increases by 2 with each subsequent term, while the power of k increases linearly with each subsequent term.
So, to find the nth term, we observe that for every term, the power of k is (n - 1), and the power of p is (2n + 1). Therefore, the nth term can be written as:
Tn = k^(n - 1)p^(2n + 1)
Now, to find the 9th term, we substitute n = 9 in the above formula:
T9 = k^(9 - 1)p^(2(9) + 1) = k^8p^19
To simplify T9, we can substitute KP = 10:
T9 = (10)^8p^19 = 10^8p^19
So, the simplified form of the 9th term is 10^8p^19.
If KP = 10, then we substitute p = 10/K in the simplified form of T9:
T9 = 10^8(10/K)^19 = 10^8 * 10^19 * K^(-19) = 10^(8 + 19) * K^(-19) = 10^27 * K^(-19)
Therefore, if KP = 10, the result becomes 10^27 * K^(-19).