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Problem
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answer type
Numerical
is multiple answer
false
language
English
question
A geometric sequence has first term 10 and common ratio .
An arithmetic sequence has first term 10 and common difference .
The ratio of the 6th term in the geometric sequence to the 4th term in the geometric sequence equals the ratio of the 6th term in the arithmetic sequence to the 4 th term in the arithmetic sequence.
Determine all possible values of .
(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence.
A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant, called the common ratio. For example, is a geometric sequence with three terms.)
Plain-text mathematical notation (without MathML)
A geometric sequence has first term 10 and common ratio (1)/(2). An arithmetic sequence has first term 10 and common difference d. The ratio of the 6th term in the geometric sequence to the 4th term in the geometric sequence equals the ratio of the 6th term in the arithmetic sequence to the 4 th term in the arithmetic sequence. Determine all possible values of d. (An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence. A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant, called the common ratio. For example, 3,6,12 is a geometric sequence with three terms.)
Original LaTeX notation
A geometric sequence has first term 10 and common ratio $\frac{1}{2}$.
An arithmetic sequence has first term 10 and common difference $d$.
The ratio of the 6th term in the geometric sequence to the 4th term in the geometric sequence equals the ratio of the 6th term in the arithmetic sequence to the 4 th term in the arithmetic sequence.
Determine all possible values of $d$.
(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence.
A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant, called the common ratio. For example, $3,6,12$ is a geometric sequence with three terms.)question type
Open-ended
subject
Math
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