Maths-
General
Easy
Question
Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....
Hint:
- Recursive Formula is a formula that defines the each term of sequence using the previous/preceding terms.
The correct answer is: a_n=a_(n-1)-8.
Explanation:
- We have given a sequence 47,39,31,23,15,...
- We have to find the recursive formula.
Step 1 of 1:
We have given a sequence 47, 39, 31, 23, 15, ....
The given sequence is an AP.
We know that the recursive formula for any AP is
, where d is common difference.
Here the common difference is - 8
So, The recursive formula is
![a subscript n equals a subscript n minus 1 end subscript plus d](data:image/png;base64,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)
![a subscript n equals a subscript n minus 1 end subscript minus 8](data:image/png;base64,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)
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![straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction](data:image/png;base64,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)
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Write an explicit formula for the arithmetic sequence.
![a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAARCAYAAACb3u1RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAkFJREFUeNrtWr9LAzEUDkVExMVBHDociIg4iJuIu0Nx6FocC+Lg7iAdxMXZTRykiAhSpENxK+LgUBAREfEfcChCBxEREc4X+oTzyLW5XH7e3YNvyJE2X768e3l5OUJy022rgAbgHfANeABsxPyPdYCfcR3nADXULzfDdgOoACawvQC4xWc8Rn/3nDs1OQVs5jqotSTieoBHzr5HgGq+mHy6FwB7gG5gW/QMEbWJiw6npvbFmbq0BcZzUU8purcAh4BJFOECUE442DDo4mK7U69gCjLIRjGaewPGO8fnZYvXVpvuFZxo0OqAkgHnsImLDqceA3QwCg+yA8D2kPFYTu2qnol1v8ZoET7QmNiibOKiOlrRyNkErA3pt8iI5L7jesqK9pH9PnFbCuZgH4ZIq+BiY6SeQYee5ejbYfTjHc+mtdWq+xvjQHJvyDlMcxGtf8ZZyHnAMWBckhPJ0tPF2m/k/F8xt/szOrGGIZKmuYjWP3n7T2OOO6JpZ4ijp4u130iu+6Rf/yxgrnUGuIro+0L6N1p3WB7akUzSFi6qnLqFkZo3OscZj3VQjKOnjEqOVWnfLkaQGr7ZXUbZhwrzg290EbAE6CkgagMXX+Ei8KQRspyaV0/XnFooj59iPFvGqBjMz9oaJpCEi2gu6uqNHXXskoCeaZi7kNGaZz3UPkkpFxcXlu5WTxrz9VQYvZXaCrWrKeXi4sIW8SBKcqfmt8vQ1tYk5m6mVHPJ8gdDmZp7j/wvD4XbaeBi8iLBycOXbfYLk7UPgKAaNAEAAAEZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPmE8L21pPjxtaT5uPC9taT48L21zdWI+PG1vPj08L21vPjxtc3ViPjxtaT5hPC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1Yj48bW8+KzwvbW8+PG1uPjIuNDwvbW4+PG1vPjs8L21vPjxtc3ViPjxtaT5hPC9taT48bW4+MTwvbW4+PC9tc3ViPjxtbz49PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21hdGg+1catWwAAAABJRU5ErkJggg==)
Write an explicit formula for the arithmetic sequence.
![a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAARCAYAAACb3u1RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAkFJREFUeNrtWr9LAzEUDkVExMVBHDociIg4iJuIu0Nx6FocC+Lg7iAdxMXZTRykiAhSpENxK+LgUBAREfEfcChCBxEREc4X+oTzyLW5XH7e3YNvyJE2X768e3l5OUJy022rgAbgHfANeABsxPyPdYCfcR3nADXULzfDdgOoACawvQC4xWc8Rn/3nDs1OQVs5jqotSTieoBHzr5HgGq+mHy6FwB7gG5gW/QMEbWJiw6npvbFmbq0BcZzUU8purcAh4BJFOECUE442DDo4mK7U69gCjLIRjGaewPGO8fnZYvXVpvuFZxo0OqAkgHnsImLDqceA3QwCg+yA8D2kPFYTu2qnol1v8ZoET7QmNiibOKiOlrRyNkErA3pt8iI5L7jesqK9pH9PnFbCuZgH4ZIq+BiY6SeQYee5ejbYfTjHc+mtdWq+xvjQHJvyDlMcxGtf8ZZyHnAMWBckhPJ0tPF2m/k/F8xt/szOrGGIZKmuYjWP3n7T2OOO6JpZ4ijp4u130iu+6Rf/yxgrnUGuIro+0L6N1p3WB7akUzSFi6qnLqFkZo3OscZj3VQjKOnjEqOVWnfLkaQGr7ZXUbZhwrzg290EbAE6CkgagMXX+Ei8KQRspyaV0/XnFooj59iPFvGqBjMz9oaJpCEi2gu6uqNHXXskoCeaZi7kNGaZz3UPkkpFxcXlu5WTxrz9VQYvZXaCrWrKeXi4sIW8SBKcqfmt8vQ1tYk5m6mVHPJ8gdDmZp7j/wvD4XbaeBi8iLBycOXbfYLk7UPgKAaNAEAAAEZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPmE8L21pPjxtaT5uPC9taT48L21zdWI+PG1vPj08L21vPjxtc3ViPjxtaT5hPC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1Yj48bW8+KzwvbW8+PG1uPjIuNDwvbW4+PG1vPjs8L21vPjxtc3ViPjxtaT5hPC9taT48bW4+MTwvbW4+PC9tc3ViPjxtbz49PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21hdGg+1catWwAAAABJRU5ErkJggg==)
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence. ![a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10](data:image/png;base64,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)
Write an explicit formula for the arithmetic sequence. ![a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10](data:image/png;base64,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)
Maths-General
Maths-
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x over denominator 2 x plus 1 end fraction](data:image/png;base64,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)
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x over denominator 2 x plus 1 end fraction](data:image/png;base64,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)
Maths-General
Maths-
The cost to rent a bike is
28 for the first day plus
2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?
The cost to rent a bike is
28 for the first day plus
2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?
Maths-General
Maths-
The daily attendance at an amusement park after day x is given by the function
f(x) =
. On Approximately which day will the attendance be 1125 people ?
The daily attendance at an amusement park after day x is given by the function
f(x) =
. On Approximately which day will the attendance be 1125 people ?
Maths-General
Maths-
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction](data:image/png;base64,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)
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Graph each function and identify the horizontal and vertical asymptotes
![r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2](data:image/png;base64,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)
Graph each function and identify the horizontal and vertical asymptotes
![r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2](data:image/png;base64,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)
Maths-General
Maths-
Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3
Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3
Maths-General