जर अंकगणिती श्रेणीत पहिल्या p पदांची बरीचही परीक्षा q पदांच्या बरीजवर असेल, तर त्यांच्यातील पहिल्या (p + q) पदांची बरीज शून्य असते हे दाखवा. जर अंकगणिती श्रेणीत पहिल्या p पदांची बरीचही परीक्षा q पदांच्या बरीजवर असेल, तर त्यांच्यातील पहिल्या (p + q) पदांची बरीज शून्य असते हे दाखवा.
Understand the Problem
हे प्रश्न अंकगणिताच्या वस्तूंच्या गुणांचा विचार करत आहे. जर दोन वस्तू (p आणि q) असतील आणि त्यांची गुणांची तुलना केली तर त्यांचे गुणांक शून्य असले तरी पिचकण्याची प्रमाणपत्रे विचारलं जात आहे.
Answer
If $q = 14$, then $p = 1$. The relationship is $p = \frac{q}{14}$.
Answer for screen readers
The relationship derived from the equation is: $$ p = \frac{q}{14} $$
Steps to Solve
- Understanding the Given Information
We have two objects $p$ and $q$ and their coefficients are being compared. The question states that if $p$ and $q$ are the first and second objects respectively, we need to examine the equation.
- Interpreting the Equation
The first part of the equation shows the ratio of the coefficients. The mathematical representation is: $$ \frac{p}{q} = \frac{1}{14} $$ This means that for every 1 unit of object $p$, there are 14 units of object $q$.
- Establishing the Relationship
Now, considering the condition that the quantities are in a direct ratio, we can multiply both sides by $q$ to establish the relationship: $$ p = \frac{1}{14} q $$
- Determining the Values Involved
Next, substitute a known value into the relationship or measure $q$ based on the given conditions. Assuming $q = 14$, we can calculate the value for $p$: $$ p = \frac{1}{14} \times 14 = 1 $$
- Verifying the Coefficients
To verify if the relationship holds, we can check the given condition of the coefficients being zero: For the condition to hold, if the ratio is correctly maintained, then: $$ p = q \cdot \frac{1}{14} $$
The relationship derived from the equation is: $$ p = \frac{q}{14} $$
More Information
In this case, if $q = 14$, then $p$ will equal 1, maintaining the ratio of 1:14. This indicates that the two objects are directly proportional under the given conditions.
Tips
- Misinterpreting Ratios: Some might confuse the ratio as a direct sum rather than a multiplicative comparison.
- Not Simplifying Equations: If one fails to simplify the ratio properly, it can lead to incorrect conclusions about the relationship.
AI-generated content may contain errors. Please verify critical information
