The positive numbers e and f are the 2nd and 14th terms respectively of an arithmetic progression whose first term is 1.It is also given that e,9 and f are three consecutive terms of a geometric progression. Find the values of e and f. ?
The values are
Then,
Then,
Therefore,
#d=(-14+-66))/(26)
Keeping only the positive value
Therefore,
and
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To find the values of and , we can use the given information about arithmetic and geometric progressions.
Given that and are the 2nd and 14th terms, respectively, of an arithmetic progression with a first term of 1, we can use the formula for the nth term of an arithmetic progression:
Where is the common difference of the arithmetic progression.
Next, we're given that , 9, and are three consecutive terms of a geometric progression. Therefore:
Where is the common ratio of the geometric progression.
Now, we can solve the system of equations:
Solving these equations will give us the values of and .
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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