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The 5th Term of an A.P. is thrice the 2nd term and the 12th term exceeds the 6th term by 1 . Find the 16nth 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 Tn=a+(n1)d to find the Nth 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 Nth term , we will have to use the formula Tn=a+(n1)d , where
 Tn - Value of Nth term
 a - 1st term of the given series
 n - No. of terms in the Series
 d - common difference between 2 consecutive terms in the series
Considering the first statement of the numerical, we can form the following equations
 T5=a+4d...............(1)
 T2=a+d.................(2)
Given that T5=3×T2
From Equation1&Equation2 we can form the following relation
 a+4d=3×(a+d)...........(3)
 a+4d=3a+3d...........(4)
 d=2a...........(5)
Considering second statement in the numerical ,we can form following equations
 T12=a+11d............(6)
 T6=a+5d............(7)
It is given that T12T6=1.............(8)
Substituting values of Misplaced & in Equation8 we get the following equation
 (a+11d)(a+5d)=1
11d5d=1
d=16
We can use Equation5 to find the value of a .
 a=16×2=13
Since we have the value of a&d we can now find the 16th term
 T16=a+15d
Substituting values of a&d we get the final value of 16th term
 T16=13+15×16
In order to simplify the sum we can multiply the numerator and denominator of 13 by 2 , so that we have a common denominator.
 T16=26+156
 T16=176
Thus the final Answer is T16=176
So, the correct answer is “T16=176”.

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 Nth 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.