Write a recursive rule for the sequence. Assume it starts with the 1st term. 10, 14, 18, 21... A. f(0) =3;F(n)=F(n - 1)+3 B. f(0) =4;F(n)=F(n - 1)+4 C. f(0) =14c;F(n)=F(n - 1) - 26 D.f(0) =6;F(n)=F(n - 1)+4

1 answer
Question:

Write a recursive rule for the sequence. Assume it starts with the 1st term. 10, 14, 18, 21...
A. f(0) =3;F(n)=F(n - 1)+3
B. f(0) =4;F(n)=F(n - 1)+4
C. f(0) =14c;F(n)=F(n - 1) - 26
D.f(0) =6;F(n)=F(n - 1)+4

Answers

Option D is correct. The correct option for the recursive formula is [tex]f(0) =6;f(n)=f(n - 1)+4[/tex]Given the sequence 10, 14, 18...The first term is 10, hencea1 = 10The previous terms will be [tex]a_{n-1}[/tex]From the sequence, we can see that 4 is being added to the previous term to get the next term. Hence the nth term will be expressed as:[tex]a_n = a_{n-1} + 4[/tex]Get the term before the first term [tex]a_0[/tex]If n = 1[tex]a_1 = a_{1-1} + 4\\a_1 = a_{0} + 4\\a_0=a_1-4\\a_0=10-4\\a_0=6[/tex]Hence the correct option for the recursive formula is [tex]f(0) =6;f(n)=f(n - 1)+4[/tex]Learn more here: https://brainly.com/question/18233843

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