f(n)=64+6n Complete the recursive formula of f(n). {:[f(1)=],[f(n)=f(n-1)+]:}

Identifying the Pattern: To find the recursive formula for the sequence, we need to express f(n) in terms of f(n-1). Let's start by calculating the first few terms of the sequence to identify the pattern. f(1) = 64 + 6(1) = 64 + 6 = 70 f(2) = 64 + 6(2) = 64 + 12 = 76 f(3) = 64 + 6(3) = 64 + 18 = 82Finding the Constant Difference: Now, let's find the difference between consecutive terms to see if it's constant. f(2) - f(1) = 76 - 70 = 6 f(3) - f(2) = 82 - 76 = 6 The difference is constant and equal to 6, which is the coefficient of n in the original formula.Writing the Recursive Formula: Using the pattern we've identified, we can write the recursive formula. Since the difference between consecutive terms is 6, we can express f(n) as f(n-1) plus this difference. So, the recursive formula is: f(1) = 70 f(n) = f(n-1) + 6 for n > 1

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f(n)=64+6n
Complete the recursive formula of
f(n).

{:[f(1)=],[f(n)=f(n-1)+]:}

$f(n)=64+6 n$ $\newline$ Complete the recursive formula of $f(n)$ . $\newline$ $\begin{array}{l} f(1)=\square \\ f(n)=f(n-1)+ \end{array}$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

f(n)=64+6 n

\newline

Complete the recursive formula of

f(n)

\newline

\begin{array}{l} f(1)=\square \\ f(n)=f(n-1)+ \end{array}

Identifying the Pattern: To find the recursive formula for the sequence, we need to express $f(n)$ in terms of $f(n-1)$ . Let's start by calculating the first few terms of the sequence to identify the pattern. $f(1) = 64 + 6(1) = 64 + 6 = 70$ $f(2) = 64 + 6(2) = 64 + 12 = 76$ $f(3) = 64 + 6(3) = 64 + 18 = 82$
Finding the Constant Difference: Now, let's find the difference between consecutive terms to see if it's constant. $\newline$ $f(2) - f(1) = 76 - 70 = 6$ $\newline$ $f(3) - f(2) = 82 - 76 = 6$ $\newline$ The difference is constant and equal to $6$ , which is the coefficient of $n$ in the original formula.
Writing the Recursive Formula: Using the pattern we've identified, we can write the recursive formula. Since the difference between consecutive terms is $6$ , we can express $f(n)$ as $f(n-1)$ plus this difference. $\newline$ So, the recursive formula is: $\newline$ $f(1) = 70$ $\newline$ f(n) = f(n-1) + 6 \text{ for } n > 1