# 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 ( e ) and ( f ), we can use the given information about arithmetic and geometric progressions.

Given that ( e ) and ( f ) 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:

[ e = 1 + (2-1)d ] [ f = 1 + (14-1)d ]

Where ( d ) is the common difference of the arithmetic progression.

Next, we're given that ( e ), 9, and ( f ) are three consecutive terms of a geometric progression. Therefore:

[ f = e \times r ] [ 9 = e \times r^2 ]

Where ( r ) is the common ratio of the geometric progression.

Now, we can solve the system of equations:

[ e = 1 + (2-1)d ] [ f = 1 + (14-1)d ] [ f = e \times r ] [ 9 = e \times r^2 ]

Solving these equations will give us the values of ( e ) and ( f ).

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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.

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