The term of the A.P. 3, 15, 27, 39.... that will be 120 more than its 21st term is ____st.

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Detailed Solution

               Concept: The term of the A.P. 3, 15, 27, 39.... that will be 120 more than its 21st term is 31st.
       First of all, “What is an Arithmetic Progression?”
       The answer comes as: An Arithmetic Progression (A.P.) is an arithmetic sequence (of        numbers) in which the difference between two consecutive terms is always constant.        For Example, 2,4,6,8,10 are in Arithmetic Progression.
       The First term of an A.P. is typically denoted by “a”.
While the Last term of an A.P. is denoted by “l”.
The common difference of an A.P. is the constant difference between two consecutive terms (as mentioned earlier in the definition of arithmetic progression) and is typically denoted by “d”.
       Finally, to find a certain xth term of an A.P., we need to use the formula of

.
Given, 3, 15, 27, 39.... are in A.P.
Therefore, in this case, (a = 3) , and (d = 12) .
As per formula mentioned above, 21st term of this A.P. =