The first two rows of coefficients are identical, so by inspection, the determinant is 0.
A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. What is the next term in
2 answers:
Answer:
The next term in the sequence is 3.
Step-by-step explanation:
Given : A sequence is defined recursively by the formula . The first term of the sequence is -1.5.
To find : What is the next term in the sequence?
Solution :
The recursive formula is
We have given,
We have to find f(2)
So, Substitute n=1 in the recursive formula,
Therefore, The next term in the sequence is 3.
You might be interested in
Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>Step-by-step explanation:
Given the function j(x) = 11.6 and k(x) =
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) =
are inverse functions.