
The Term of an A.P. is thrice the term and the term exceeds the term by . Find the Term.
Answer
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Hint: After having a look we can identify that this is a sum from the Arithmetic Progression. First step in solving such a sum is to understand each and every statement and then think of the correct formula which can be applied. Based on the given data we can apply the formula to find the term. In order to solve these problems we will have to pick up 1 statement at a time and then form equations accordingly.
Complete step-by-step answer:
Since this sum involves finding the value of term , we will have to use the formula , where
- Value of term
- term of the given series
- No. of terms in the Series
- common difference between consecutive terms in the series
Considering the first statement of the numerical, we can form the following equations
Given that
From we can form the following relation
Considering second statement in the numerical ,we can form following equations
It is given that
Substituting values of in we get the following equation
We can use to find the value of .
Since we have the value of we can now find the term
Substituting values of we get the final value of term
In order to simplify the sum we can multiply the numerator and denominator of by , so that we have a common denominator.
Thus the final Answer is
So, the correct answer is “ ”.
Note: Though this sum may look complicated or lengthy , it is not at all difficult as we have applied only 1 formula several times . In numericals related to arithmetic progression it is advantageous to learn the formula of Sum upto term also . These are the only 2 formulas based on which the questions are asked. Students are advised not to panic if the question is long or difficult to comprehend, it will become pretty simple if they break down multiple statements into smaller ones and start solving.
Complete step-by-step answer:
Since this sum involves finding the value of
Considering the first statement of the numerical, we can form the following equations
Given that
From
Considering second statement in the numerical ,we can form following equations
It is given that
Substituting values of
We can use
Since we have the value of
Substituting values of
In order to simplify the sum we can multiply the numerator and denominator of
Thus the final Answer is
So, the correct answer is “
Note: Though this sum may look complicated or lengthy , it is not at all difficult as we have applied only 1 formula several times . In numericals related to arithmetic progression it is advantageous to learn the formula of Sum upto
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