Maths-
General
Easy
Question
Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...
Hint:
- A sequence is said to be arithmetic if the common difference is always constant.
- The General formula of any AP is
.
The correct answer is: ⇒-13
Explanation:
- We have given a sequence 77,64,51,38,25,...
- We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 77,64,51,38,25,..
The difference in first two terms is
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 64 minus 77 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table](data:image/png;base64,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)
Now the difference in next two terms is
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 51 minus 64 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table](data:image/png;base64,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)
Then, The difference between next two terms will be
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 38 minus 51 end cell row cell not stretchy rightwards double arrow negative 13 end cell end table](data:image/png;base64,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)
Since the difference is constant
The given sequence is an arithmetic sequence.
Now the difference in next two terms is
Then, The difference between next two terms will be
Since the difference is constant
The given sequence is an arithmetic sequence.
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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 x over denominator x minus 6 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 x over denominator x minus 6 end fraction](data:image/png;base64,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)
Maths-General
Maths-
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,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)
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,iVBORw0KGgoAAAANSUhEUgAAAKEAAAARCAYAAAC1m8zDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAnNJREFUeNrtWb9LQzEQfhQpDkUoUjo4CA6O4iYiIi5FRKQIDp1EBHF0cygdxH9AHAQRKSJSkCIOIi5SHAURBwdxcXIoQgeRUkpBL/QqISavafvy69EPviFp2nd3uZfcffW8PnRjHngDrAJrwDfgPnDYUX/GgTngs8+aIeAh8AF5hHN9GEIJuAKMUnOTwFtH/TkDbgJ/fNbcAZep8RLO9WEZvhy3X5SEq8ADzjw5/TPsZAS4CywD63i8jhpyyCZbdGAM+Op4bERJWASmBGVJkZ28xoyNo6MXwHSPRrWjCEHbYiuSwHWsCxeZzwoYo7TF+ySThBWm9Gghii/SHzLoDI1TTmB0wCZbVJ4aNLc5a3hJaHNsREnY8PlOnS2Wp5kF94aOeZtsUX2CxDHJSMc453hsuknCGj2o4tFO1x3fhjZJhS22I4aJ2A427ZNsEpYF1/Egex1/MgtmgE+GNsS0LTK6lwrUAo6Nbj/8GpMFznyKbUw+MDNbyPE6F00wbYuM7hU0JrA5CTI2uv0QPYdoosec+Twr0ex5TRU7gvXFuddU9XkgUgIRGx+xsNwJ2BlbbFG1eaSGI9rZAPpIpIp34JpEY9JJbFT70clzSth8DeDVnMU4/EMWO68cdV+nORpVA9+yEa+p9FcUOGSDLao2bxZllhqyhC+STHcsGxudSShTQ5IG7AT9reKLFJP58QRnbgpPHbom0fH3Sy+2dFtw67yORShIyC8JB/wIFBnUpehxPqS2mN48crK/4BXmsh+Bgyj1W8x4I6S2mN48UmIkQ+BH4Lhkrocrz5xar9qWsGxe6JKwwkgE7DgMtnQr1tqYfE748Qv8TP3RNq2SKgAAAQ50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+YTwvbWk+PG1pPm48L21pPjwvbXN1Yj48bW8+PTwvbW8+PG1zdWI+PG1pPmE8L21pPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3ViPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM8L21uPjxtbz47PC9tbz48bXN1Yj48bWk+YTwvbWk+PG1uPjE8L21uPjwvbXN1Yj48bW8+PTwvbW8+PG1uPjEwPC9tbj48L21hdGg+awzmUwAAAABJRU5ErkJggg==)
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