Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer:
F(n)=3(n-1)+25; F(12)=58
Step-by-step explanation:
A sequence is arithemetic if the difference of any two consecutive terms in the sequence is always the same constant term.A recursive way to construct an arimethic sequence is to take an initial number [tex]a_1[/tex] an then recursively sum a positive number (distance) [tex]d[/tex] to get each term, for example take [tex]a_1=1[/tex] and [tex]d=2[/tex], we get the terms of the arithmetic sequence:
[tex]a_1=1\\a_2=1+2\\a_3=1+2+2=1+2\cdot2\\a_4=1+2+2+2=1+2\cdot 3\\a_5=1+2+2+2+2=1+2\cdot 4[/tex]
and in general the n-th term of the sequence is given by the equation
[tex]a_n=1+2\cdot(n-1)=a_1+d\cdot(n-1)[/tex].
Note that g(n)=3(n-1) is already an arithmetic sequence with [tex]a_1=0[/tex] and [tex]d=3[/tex] and f(n) is the constant function with constant value equals to 25.
Hence, if we take
[tex]F(n)=f(n)+g(n)=25+3\cdot(n-1)[/tex]
we get an arithmetic sequence with intial value [tex]a_1[/tex] equals to 25 and distance [tex]d[/tex] equals to 3.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.