More Practice With Recursive and Arithmetic Formulas

Given the recursive formula of an arithmetic sequence is:

$$a\left(1\right)=14$$

$$a\left(n\right)=a\left(n-1\right)+6$$

What is the 1st term?

(a)  

Given the recursive formula of an arithmetic sequence is:

$$a\left(1\right)=14$$

$$a\left(n\right)=a\left(n-1\right)+6$$

What is the common difference?

Hint: The recursive formula for an arithmetic sequence provides the 1st term $$a\left(1\right)$$ and a rule for finding the nth term $$a\left(n\right)$$ using the previous (n-1)th term $$a\left(n-1\right)$$ and the common difference $$d$$ such that $$a\left(n\right)=a\left(n-1\right)+d$$ .

(a)  

Given the recursive formula of an arithmetic sequence is:

$$a\left(1\right)=14$$

$$a\left(n\right)=a\left(n-1\right)+6$$

What is the 3rd term $$a\left(3\right)$$ ? Just type the numerical value for $$a\left(3\right)$$ .

Hint: Given the recursive formula for an arithmetic sequence, we need to find the 2nd term $$a\left(2\right)$$ before we can find the 3rd term $$a\left(3\right)$$ .

(a)  

Given that the explicit formula of an arithmetic sequence is of the form $$a\left(n\right)=a\left(1\right)+\left(n-1\right)d$$ ,

what is the explicit formula for the arithmetic sequence with the recursive formula

$$a\left(1\right)=14$$

$$a\left(n\right)=a\left(n-1\right)+6$$ ?

Given the explicit formula of an arithmetic sequence is $$a\left(n\right)=14+\left(n-1\right)\left(6\right)$$ , what is the 51st term $$a\left(51\right)$$ ?

Hint: Replace $$n$$ in the explicit formula with $$51$$ , then simplify the right side of the formula.

Your answer should be a whole number.

(a)  

Given the explicit formula of an arithmetic sequence is of the form $$a\left(n\right)=a\left(1\right)+\left(n-1\right)\left(d\right)$$ , what is the recursive formula for the arithmetic sequence with the explicit formula $$a\left(n\right)=-12+\left(n-1\right)\left(-2\right)$$ ?

Hint: The recursive formula for an arithmetic sequence provides the 1st term $$a\left(1\right)$$ and provides a rule for finding the nth term in terms of the previous (n-1)th term and the common difference d where $$a\left(n\right)=a\left(n-1\right)+d$$

Select the explicit formula which represents the following arithmetic sequence:

$$-8,\ -9,\ -10,\ -11,\ -12,\ .\ .\ .$$

Hint: The explicit formula of an arithmetic sequence is of the form $$a\left(n\right)=a\left(1\right)+\left(n-1\right)\left(d\right)$$ where $$a\left(1\right)$$ is the 1st term of the sequence and $$d$$ is the common difference obtained by subtracting any term from the term which follows it.

Given the explicit formula for an arithmetic sequence is $$a\left(n\right)=20+\left(n-1\right)\left(-1\right)$$ , which 2 of the following choices represents a simplified form of the given explicit formula after applying the distributive property and combining like terms on the right side of the given explicit formula?