Question

whats the common difference between 3,3/2,3/4

Answer 1

Question :- whats the common difference between 3,3/2,3/4 .?

Solution :-

given that,

• first term = 3
• second term = 3/2
• third term = 3/4 .

we know that, if the series in AP ,

• common difference = second term - first term = third term - second term .
• we have to subtract each term from the subsequent term to determine whether a common difference exists.

so,

→ second term - first term

→ (3/2) - 3

→ (3 - 6)/2

→ (-3/2) .

and,

→ third term - second term

→ (3/4) - (3/2)

→ (3 - 6)/4

→ (-3/4)

since,

→ (-3/2) ≠ (-3/4) .

therefore, we can conclude that, the given sequence is not arithmetic because there is no common difference.

_____________

Correct Question :- whats the common ratio between 3,3/2,3/4 ?

Solution :-

common ratio :-

• second term / first term .
• third term / second term.

so,

→ second term / first term

→ (3/2) ÷ 3

→ (3/2) * (1/3)

→ (1/2) .

and,

→ third term / second term

→ (3/4) ÷ (3/2)

→ (3/4) * (2/3)

→ (1/2) .

Hence, the common ratio between given terms is (1/2).

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Answer 2

SOLUTION

TO DETERMINE

The common difference between

$\displaystyle \sf{3 \:, \: \frac{3}{2} \: , \: \frac{3}{4} }$

EVALUATION

Here the given terms are

$\displaystyle \sf{3 \:, \: \frac{3}{2} \: , \: \frac{3}{4} }$

Now Second Term - First term

$\displaystyle \sf{ = \frac{3}{2} - 3 }$

$\displaystyle \sf{ = \: - \frac{3}{2} \: }$

Third term - Second term

$\displaystyle \sf{ = \frac{3}{4} - \: \frac{3}{2} }$

$\displaystyle \sf{ = - \frac{3}{4} }$

Hence common difference does not exists

CORRECT QUESTION

TO DETERMINE

The common ratio between

$\displaystyle \sf{3 \:, \: \frac{3}{2} \: , \: \frac{3}{4} }$

Here

Second Term / First term

$\displaystyle \sf{ = \frac{1}{2} }$

Third term / Second term

$\displaystyle \sf{ = \frac{1}{2} }$

Hence the required common ratio

$\displaystyle \sf{ = \frac{1}{2} }$

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