Let us understand Arithmetic Progression with the help of a sample numerical. Click on the link to Watch the VIDEO: Watch Video
Numerical
Problem : If the A.P. is 3, 10, 17, and 63, 65, 67 and So on have the same nth term, then what is the value of n?
Solution: Consider the A.P. 3, 10, 17
first term is equal to a is equal to 3 and the common difference is 7
We know that, Tn is equal to a plus n minus 1 into d
Substitute the values of a and d and obtain the equation Tn
Therefore Tn is equal to 7n minus 4 let this be equation 1
Now consider the second A.P i.e., 63, 65, 67 and So on
Here a is equal to 63 and d is equal to 2
obtain the equation of Tn and by substituting the values of a and b
Therefore Tn is equal to 61 plus 2n let this be the equation 2
Given that both the A.P. have the same nth term.
Therefore, 7n minus 4is equal to 61 plus 2n this implies 7n minus 2n is equal to 61 plus 4
Now, calculate the value of n
Hence the value of n is found to be equal to 13.
Numerical
Problem : If the A.P. is 3, 10, 17, and 63, 65, 67 and So on have the same nth term, then what is the value of n?
first term is equal to a is equal to 3 and the common difference is 7
We know that, Tn is equal to a plus n minus 1 into d
Substitute the values of a and d and obtain the equation Tn
Therefore Tn is equal to 7n minus 4 let this be equation 1
Now consider the second A.P i.e., 63, 65, 67 and So on
Here a is equal to 63 and d is equal to 2
obtain the equation of Tn and by substituting the values of a and b
Therefore Tn is equal to 61 plus 2n let this be the equation 2
Given that both the A.P. have the same nth term.
Therefore, 7n minus 4is equal to 61 plus 2n this implies 7n minus 2n is equal to 61 plus 4
Now, calculate the value of n
Hence the value of n is found to be equal to 13.
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