Maths-
General
Easy
Question
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 7 semicolon a subscript 1 equals negative 3](data:image/png;base64,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)
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: a_n=4-7n.
Explanation:
- We have given
![a subscript n equals a subscript n minus 1 end subscript minus 7 comma a subscript 1 equals negative 3](data:image/png;base64,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)
- We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is
, where d is common difference.
Here we have ![a subscript n equals a subscript n minus 1 end subscript minus 7](data:image/png;base64,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)
So, d = -7
Also, We have a1 = -3
So, The explicit formula 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 a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals negative 3 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 7 right parenthesis end cell row cell a subscript n equals 4 minus 7 n. end cell end table](data:image/png;base64,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)
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Related Questions to study
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Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56](data:image/png;base64,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)
Maths-General
Maths-
Graph each function ![g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 1 end fraction](data:image/png;base64,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)
Graph each function ![g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 1 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Find the equation for a path that passes through the point (6, 6) and is perpendicular to
.
Find the equation for a path that passes through the point (6, 6) and is perpendicular to
.
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8](data:image/png;base64,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)
Maths-General
Maths-
Graph each function ![f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 end fraction](data:image/png;base64,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)
Graph each function ![f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 end fraction](data:image/png;base64,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)
Maths-General
Maths-
What is the graph of the function![f left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 end fraction](data:image/png;base64,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)
What is the graph of the function![f left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Write recursive formula and explicit formula. -15,-6,-3,12,21,...
Write recursive formula and explicit formula. -15,-6,-3,12,21,...
Maths-General
Maths-
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
Maths-General
Maths-
Write recursive formula and explicit formula. 62,57,52,47,42,...
Write recursive formula and explicit formula. 62,57,52,47,42,...
Maths-General
Maths-
Write recursive formula and explicit formula. -4, 5,14,23,32,...
Write recursive formula and explicit formula. -4, 5,14,23,32,...
Maths-General
Maths-
What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
Maths-General
Maths-
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
Maths-General